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Recognition, modeling and pricing of flexibility in construction of cave mining systems Ahmed, Haitham Magdi 2015

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RECOGNITION, MODELING AND PRICING OF FLEXIBILITY IN CONSTRUCTION OF CAVE MINING SYSTEMS by  Haitham Magdi Ahmed  B.A., Civil Engineering, King Abdul Aziz University, 2002 M.A.Sc., Mining Engineering, The University of British Columbia, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mining Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   June 2015  © Haitham Magdi Ahmed, 2015 ii  Abstract  Mass caving systems require significant capital expenditure and long-term commitment of resources before production commences. Cave mining projects are confronted with numerous challenges in maintaining their construction schedule expectations. Any delay in construction impacts on the production schedule and, in turn, reduces the project value. In order to increase the expected economic value, the construction schedule needs to be accelerated through strategic flexibilities. It is hypothesized that construction acceleration (crashing) can be achieved by prioritizing the construction schedule or changing the construction strategy.   This thesis seeks to expand current knowledge on three interrelated domains for decision making in engineering systems—(i) recognition, (ii) modeling and (iii) pricing of flexibility in cave mining construction. An objective of this study was to provide state-of-the-art project formulation techniques employed in planning that can be used to support decision-making processes in cave mining systems. The first domain requires identifying construction strategies that allow the mine management to implement construction crashing in multiple heading development. Three independent and interrelated flexibilities are considered.    The second domain requires development of a methodology suitable for investigating and forecasting through modeling the development and construction rates enabling implementation of flexible strategies. A method capable of modeling the development and construction processes with respect to the advance undercut mining strategy is developed, which integrates the geotechnical and equipment-related uncertainties, using the framework of discrete event iii  simulation.  Several models are developed to investigate the impact of implementing these flexibilities on the development and construction rates. The results from the flexible models compared to the benchmark models confirmed that significant construction benefits can be achieved.    The third domain requires development of an algorithm suitable for evaluating the cost of implementing a construction crashing option that can accommodate delays. A method that is able to respond to schedule uncertainties in construction projects by incorporating the decision-making strategy of project crashing into the budget, including the cost contingency valuation, is developed using the framework of real options and Monte Carlo simulation from a contractor’s perspective. The results indicated that significant change in costs stems from the variation in risk perceptions and confidence levels.  iv  Preface   This dissertation entitled “Recognition, Modeling and Pricing of Flexibility in Construction of Cave Mining Systems” is original and independent work by the author, Haitham Magdi Ahmed. The research conducted in this dissertation was supervised by Dr. W Scott Dunbar. All the work presented henceforth was conducted at the University of British Columbia, Vancouver Campus.   A version of Sections 2.3 and 3.11.3 has been presented and published as Ahmed HM and Dunbar WS (2013), Modeling and Pricing of Flexibility in Construction of Block Caving Operations, proceeding of 23th World Mining Congress, Montreal, Quebec, Canada. I was the lead investigator, responsible for all major area of concept formation, data collection and analysis, as well as manuscript composition. Dr. W Scott Dunbar assisted in formulating the initial problem and contributed to manuscript edits. Most of the raw data were provided by New Afton mine.   A version of Sections 2.4 and 3.11.4 has been published in the International Journal of Mining, Environment, and Reclamation [Ahmed HM, Scoble MJ, Dunbar WS (2014). A Comparison between Offset Herringbone and El Teniente Underground Cave Mining Extraction Layouts Using a Discrete Event Simulation Technique]. I was the lead investigator, responsible for all major area of concept formation, data collection and analysis, as well as manuscript composition. Dr. Malcolm Scoble and Dr. W Scott Dunbar assisted in formulating the initial problem and contributed to manuscript edits.  v  A version of Sections 2.5, 3.3 and 3.11.5 will be submitted to a journal publication [Ahmed HM, Dunbar WS, Scoble MJ. Modeling strategic flexibilities in construction of underground cave mining systems using discrete event simulation technique]. I was the lead investigator, responsible for all major areas of concept formation, data collection and analysis, as well as manuscript composition. Dr. W Scott Dunbar and Dr. Malcolm Scoble assisted in formulating the initial problem and contributed to manuscript edits.      A version of Chapter 4 will be submitted to a journal publication [Ahmed HM, Dunbar WS, Russell AD. Budget Inclusive of Contingency Estimation in Capital Projects Using Least-squares Monte Carlo Real Options]. I was the lead investigator, responsible for all major areas of concept formation, data collection and analysis, as well as manuscript composition. Dr. W Scott Dunbar and Dr. Alan Russell assisted in formulating the initial problem and contributed to manuscript edits.        vi  Table of Contents  Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iv Table of Contents ......................................................................................................................... vi List of Tables ............................................................................................................................... xii List of Figures ............................................................................................................................. xiv List of Symbols .............................................................................................................................xx List of Abbreviations ............................................................................................................... xxiii Acknowledgements ....................................................................................................................xxv Dedication ................................................................................................................................. xxvi Chapter 1: Introduction ................................................................................................................1 1.1 Overview of the Future of Mass Mining Challenges ...................................................... 1 1.2 Problems Related to Underground Development and Construction ............................... 6 1.3 Challenges to Introduce Flexibility during Construction................................................ 8 1.4 Problems Related to Capital Budget Estimation ............................................................. 9 1.5 Research Motivation ..................................................................................................... 10 1.6 Research Questions ....................................................................................................... 13 1.7 Research Objectives ...................................................................................................... 15 1.8 Research Contributions ................................................................................................. 16 1.9 The Case Study: New Afton Mine ................................................................................ 17 1.9.1 Overview ................................................................................................................... 17 1.9.2 Development and Construction Process ................................................................... 19 vii  1.9.3 Uncertainty in the Construction ................................................................................ 22 1.10 Thesis Structure ............................................................................................................ 23 Chapter 2: Recognition of Flexibility in Cave Mining Design and Construction ..................24 2.1 Introduction ................................................................................................................... 24 2.2 Literature Review.......................................................................................................... 26 2.2.1 The Context of Flexibility in the Decision-Making Process .................................... 26 2.2.2 Flexibility within the Perspective of Real Options ................................................... 28 2.2.3 Uncertainty and Risk in Mining ................................................................................ 30 2.2.4 Geotechnical and Technical Risks in Underground Mining ..................................... 31 2.2.5 Flexibility in Mining Engineering Systems .............................................................. 32 2.2.6 Summary ................................................................................................................... 37 2.3 Flexibility in the Ore Handling System ........................................................................ 38 2.3.1 The Challenges Faced During the Pre-Production Phase ......................................... 40 2.3.2 Recognition of Flexibility in Construction ............................................................... 42 2.3.3 Design Considerations for the Ore Handling System ............................................... 43 2.3.4 Current Design and Construction Challenges ........................................................... 44 2.3.5 Design Considerations for Flexibility ....................................................................... 45 Design option 1: Utilize a jaw crusher in the extraction level temporarily ...................... 46 Design option 2: Move the gyratory crusher nearby to the construction area .................. 47 Design option 3: Build two gyratory crushers in the haulage level .................................. 48 2.4 Flexibility in the Extraction Level ................................................................................ 50 2.4.1 Major Decision Factors in Extraction Level Layout Design .................................... 52 2.4.2 Extraction Level Design Considerations .................................................................. 53 viii  2.4.3 Drawpoint Spacing Considerations........................................................................... 55 2.4.4 Extraction Crosscut Development ............................................................................ 60 2.4.5 Recognition of Flexibility in Construction ............................................................... 61 2.5 Flexibility in the Undercut Level .................................................................................. 63 2.5.1 Undercut Level Design Considerations .................................................................... 67 2.5.2 Advance Undercut Strategy from Design to Construction ....................................... 72 2.5.3 Recognition of Flexibility in Construction ............................................................... 74 Option Case 1: Middle sequencing commencing from the middle of Block 1 ................. 78 Option Case 2: Middle sequencing commencing from the middle of the footprint between Block 2 and Block 3 .......................................................................................................... 78 2.6 Conclusions ................................................................................................................... 80 Chapter 3: Modeling of Flexibility in Cave Mining Construction ..........................................81 3.1 Introduction ................................................................................................................... 81 3.2 Literature Review.......................................................................................................... 82 3.2.1 Application of DES in Underground Mining............................................................ 84 3.2.2 Application of DES in Block Caving........................................................................ 86 3.3 Simulation Framework.................................................................................................. 88 3.3.1 Scope of Simulation Models ..................................................................................... 88 3.3.2 Distinction between Development and Construction Models .................................. 89 3.4 Model Evolution ........................................................................................................... 90 3.4.1 Evolution of Development Models ........................................................................... 90 3.4.2 Evolution of Construction Models ............................................................................ 94 3.5 Modeling Uncertainties ................................................................................................. 97 ix  3.5.1 Geotechnical Uncertainties ....................................................................................... 97 3.5.2 Equipment Breakdown Uncertainty .......................................................................... 98 3.6 Typical Model Setup and Assumptions ...................................................................... 100 3.6.1 Typical Development Model Build-up ................................................................... 100 3.6.2 Development Model Activities Input Parameters ................................................... 103 Ore mucking.................................................................................................................... 103 Shotcreting ...................................................................................................................... 104 Rock bolting .................................................................................................................... 105 Face drilling and blasting ................................................................................................ 105 3.6.3 Typical Construction Model Build-up .................................................................... 106 3.7 Comprehensive Model Assumptions .......................................................................... 108 3.8 The Benchmark Model Assumptions.......................................................................... 111 3.9 Scenario Model Assumptions ..................................................................................... 113 3.10 Model Verification and Validation ............................................................................. 116 3.10.1 Simulation Model Verification ........................................................................... 117 3.10.2 Simulation Model Validation .............................................................................. 117 3.11 Simulation Results ...................................................................................................... 121 3.11.1 Optimal Equipment Operation Using Dynamic Programming ........................... 121 3.11.2 Benchmark Model Results .................................................................................. 121 3.11.3 Flexibility in Ore Handling System Results ....................................................... 128 3.11.4 Flexibility in Extraction Level Results ............................................................... 135 3.11.5 Flexibility in Undercut Level Results ................................................................. 142 3.11.6 Discussion of the Results .................................................................................... 148 x  Chapter 4: Pricing of Flexibility in Cave Mining Construction ............................................151 4.1 Introduction ................................................................................................................. 151 4.2 Literature Review........................................................................................................ 153 4.3 LSM Real Options Framework ................................................................................... 157 4.4 LSM Method in Construction ..................................................................................... 158 4.4.1 LSM Method Overview and Assumptions ............................................................. 158 4.4.2 Proposed LSM Method ........................................................................................... 160 4.5 Numerical Example: Project Comprising Two Work Packages ................................. 177 4.5.1 Model Input Parameters .......................................................................................... 177 4.5.2 Model Results ......................................................................................................... 179 4.6 Flexible Scenarios: Project Comprising Seven Work Packages ................................. 182 4.6.1 Model Input Parameters .......................................................................................... 182 4.6.2 Model Convergence (Choosing H) ......................................................................... 186 4.6.3 Results for LSD Method ......................................................................................... 187 4.7 Case Study: Project Comprising Multiple Work Packages ........................................ 189 4.7.1 Model Input Parameter ........................................................................................... 189 4.7.2 Results for LSD Method ......................................................................................... 192 4.7.3 Sensitivity Analysis ................................................................................................ 195 4.8 Discussion of the Results ............................................................................................ 198 Chapter 5: Conclusions and Future work ...............................................................................199 5.1 Conclusions ................................................................................................................. 199 5.2 Future Work ................................................................................................................ 204 References ...................................................................................................................................206 xi  Appendices ..................................................................................................................................221 Appendix A Dynamic Programing Optimization Results ...................................................... 221 A.1 Equipment Utilization for Four-drawbell Advance Undercut Progress Cycle ....... 221 A.2 Equipment Utilization for Five-drawbell Advance Undercut Progress Cycle ........ 223 A.3 Equipment Utilization for Ten-drawbell Advance Undercut Progress Cycle ........ 225 Appendix B Discrete Event Simulation Results ..................................................................... 227 B.1 The Benchmark Model ........................................................................................... 227 B.2 Flexibility in the Ore Handling System .................................................................. 229 B.3 Flexibility in the Extraction Level .......................................................................... 231 B.4 Flexibility in the Undercut Level ............................................................................ 233  xii  List of Tables  Table 2.1 General comparison between Offset Herringbone and EL Teniente layouts ............... 53 Table 2.2 Comparison between side and middle sequencing specific to New Afton mine .......... 79 Table 3.1 Input modeling parameter of one development mining cycle .................................... 102 Table 3.2 Major equipment utilized in development .................................................................. 103 Table 3.3 Input modeling parameters of a typical drawbell construction................................... 107 Table 3.4 Major equipment used in construction ........................................................................ 107 Table 3.5 Development requirements for every comprehensive development model................ 111 Table 3.6 Simulation results for the development model (Scenario-ESH) ................................. 126 Table 3.7 Simulation results for the construction model (Scenario-ESH).................................. 126 Table 3.8 Simulation results for the development model (Scenario-ESV) ................................. 129 Table 3.9 Simulation results for the construction model (Scenario-ESV).................................. 129 Table 3.10 Comparison between the mean values of the benchmark and flexible models ........ 133 Table 3.11 Comparison between the mean values of the development rates for the benchmark and flexible models ..................................................................................................................... 134 Table 3.12 Simulation results:  El Teniente versus Offset Herringbone .................................... 137 Table 3.13 Comparison between the mean values of the comprehensive development models 137 Table 3.14 Simulation results for the Offset Herringbone development models (Scenario-OSH)..................................................................................................................................................... 138 Table 3.15 Simulation results for the Offset Herringbone development models (Scenario-OSV)..................................................................................................................................................... 138 Table 3.16 Comparison between the expected development targets .......................................... 141 xiii  Table 3.17 Development Cycles and Meters Required for El Teniente and Offset Herringbone Layouts ........................................................................................................................................ 142 Table 3.18 Simulation results for the middle-sequencing construction model (Scenario-EMH verse Scenario-EMV).................................................................................................................. 143 Table 3.19 Summary and comparison between the mean values of the Construction Progress Rates (Side-Sequencing verse Middle-Sequencing Cases 1 and 2) ............................................ 145 Table 4.1 Data input for a project comprising two work packages ............................................ 178 Table 4.2 Data input regarding level of delays (beta distribution parameters) for a project comprising of two work packages .............................................................................................. 179 Table 4.3 Results for the total budget, inclusive of contingency, for two work packages ......... 180 Table 4.4 Summary of discrete event simulation results and estimated beta distribution .......... 183 Table 4.5 Work, time and cost input parameters – Scenario-ESH ............................................. 184 Table 4.6 Work, time and cost input parameters – Scenario-ESV ............................................. 185 Table 4.7 Work, time and cost input parameters – Scenario-OSV ............................................. 185 Table 4.8 Work, time and cost input parameters – Scenario-ELV ............................................. 186 Table 4.9 Scope, time and cost parameters used in the LSM model for a construction project comprising multiple work packages ........................................................................................... 191 Table 4.10 Results for the budget, inclusive of contingency associated with schedule delays .. 196  xiv  List of Figures  Figure 1.1 World copper mine production from 1900 to 2012 (Source: International Copper Study Group, 2013) ......................................................................................................................... 1 Figure 1.2 Percentage of copper to concentrator by mining method from 2006 to 2018 (Source: Moss, 2011)..................................................................................................................................... 2 Figure 1.3 Current and future potential block cave mines in British Columbia, Canada (Source: Google Earth view) ......................................................................................................................... 3 Figure 1.4 Schematic diagram of an underground cave mining system, including the interconnected infrastructure levels at the bottom of the ore body ................................................. 4 Figure 1.5 Schematic 3-D diagram of an underground cave mining system, including the interconnected infrastructure levels as well as the drawbells (Moss, 2011) ................................... 5 Figure 1.6 Schematic 3-D diagram of an extraction level as associated drawbells (Moss, 2011) .. 6 Figure 1.7 Strategic and tactical role in pre-production phase ....................................................... 9 Figure 1.8 Process diagram for cave mining systems planning and design.................................. 14 Figure 1.9 North-west cross Section of the main infrastructure and geological features of New Afton mine (Source: New Afton mine, 2012) .............................................................................. 18 Figure 1.10 Isometric view of New Afton underground mine infrastructure (Source: New Afton mine, 2012) ................................................................................................................................... 18 Figure 1.11 Schematic diagram of the three phases of the development and construction .......... 19 Figure 1.12 Plan view of New Afton infrastructure completed during construction phase (Source: New Afton mine, 2012) ................................................................................................................ 20 xv  Figure 2.1 Plan view of the New Afton haulage level including crusher complex and conveyor chamber (black circle) (Source: New Afton mine 2012) .............................................................. 39 Figure 2.2 Three design options for the ore handling system (plan view) ................................... 49 Figure 2.3 El Teniente and Offset Herringbone layout designs (plan view) ................................ 50 Figure 2.4 Extraction level design parameters – A: distance between draw zone in drawbell, B: distance of draw zones across minor Apex, C: distance of draw zones across major Apex, D: width of extraction drive, and E: distance between two extraction drives (pillar) ....................... 55 Figure 2.5 Plan view of New Afton El Teniente extraction layout (Source: New Afton mine, 2012) ............................................................................................................................................. 58 Figure 2.6 Plan view of New Afton mine extraction levels – the 100th completed on 27th may 2014 (Source: New Gold, 2014) ................................................................................................... 59 Figure 2.7 Comparison between Offset Herringbone and El Teniente layouts – in terms of drifting cycles, turnouts and intersections (plan view) ................................................................. 60 Figure 2.8 Cross section (North-South) of New Afton horizontal levels – apex, undercut and extraction levels are 17 m apart (Source: New Afton mine, 2012) .............................................. 64 Figure 2.9 Plan view of New Afton Undercut level – undercut advances from west to east (Source: New Afton mine 2012) ................................................................................................... 65 Figure 2.10 Plan view of New Afton Apex level– 17 m above the undercut level (Source: New Afton mine, 2012) ......................................................................................................................... 66 Figure 2.11 Schematic diagram showing suitable undercut drives and undercut face direction with respect to major structural discontinuities and major horizontal stress (plan view) ............. 69 Figure 2.12 Process diagram of the sequencing of the “Advance Undercut Strategy” (Elevation)....................................................................................................................................................... 71 xvi  Figure 2.13 Advance undercut strategy - production, constriction, and development zones (Elevation)..................................................................................................................................... 72 Figure 2.14 Side-sequencing and Middle-sequencing cases 1 and 2 (plan view) ........................ 77 Figure 3.1 Evolution of development models (typical, comprehensive, and scenario models) ... 91 Figure 3.2 Side-sequencing and Middle-sequencing strategies (plan view of New Afton ore body footprint) ....................................................................................................................................... 93 Figure 3.3 El Teniente and Offset herringbone layout designs (plan view) ................................. 94 Figure 3.4 Evolution of construction models (typical, comprehensive, and scenario models) .... 95 Figure 3.5 (Top) sequential operating activities of a drifting cycle; (Bottom) non-sequential non-operating activities of a drifting cycle ........................................................................................ 100 Figure 3.6 Advance undercut progress cycles - early stage of construction ramp-up (plan view)..................................................................................................................................................... 109 Figure 3.7 Number of drawbells constructed in every AUPC for side-sequencing scenarios .... 112 Figure 3.8 Advance undercut progress cycles for side-sequencing scenarios – subsequent AUPC shown in different color (plan view) ........................................................................................... 113 Figure 3.9 Number of drawbells constructed in every AUPC for middle-sequencing scenarios 115 Figure 3.10 Advance undercut progress cycles for middle-sequencing scenarios – subsequent AUPC shown in different color (plan view) ............................................................................... 115 Figure 3.11 Comparison of actual development performance with development models ......... 118 Figure 3.12 Comparison of actual construction performance with construction models ........... 120 Figure 3.13 Completion times for one progress cycle requirement in the CDM-EH-2M model - one random simulation run for AUPC-1 ..................................................................................... 122 xvii  Figure 3.14 Completion times for one progress cycle requirement in model (CDM-EH-6M) - one random simulation run for AUPC-5 ........................................................................................... 123 Figure 3.15 Completion times for full-construction phase requirements in one progress cycle (one random simulation run for CCM-SH-5M) .......................................................................... 124 Figure 3.16 Simulation results for the development and construction models (Scenario-ESH) 125 Figure 3.17 Beta PDF and CDF for the development model (Scenario-ESH) ........................... 127 Figure 3.18 Beta PDF and CDF for the construction model (Scenario-ESH) ............................ 127 Figure 3.19 Comparison between simulation results for the development models (Scenario-ESH verse Scenario-ESV) ................................................................................................................... 130 Figure 3.20 Comparison between simulation results for the construction models (Scenario-ESH verse Scenario-ESV) ................................................................................................................... 131 Figure 3.21 Beta PDF and CDF for the development model (Scenario-ESV) ........................... 132 Figure 3.22 Beta PDF and CDF for the construction model (Scenario-ESV) ............................ 132 Figure 3.23 Comparison between extraction crosscut completion times for one AUPC ........... 133 Figure 3.24 Completion times for one progress cycle requirement in the Offset Herringbone development model - one random simulation run for AUPC-1 .................................................. 136 Figure 3.25 Simulation results for the development strategies:  Offset Herringbone versus El Teniente layout............................................................................................................................ 139 Figure 3.26 Beta CDF and PDF for extraction level Offset Herringbone model (truck-haul system) ........................................................................................................................................ 140 Figure 3.27 Beta CDF and PDF for extraction level Offset Herringbone model (conveyor system)..................................................................................................................................................... 140 Figure 3.28 Beta CDF and PDF for middle-sequencing models:  (truck-haul system) .............. 144 xviii  Figure 3.29 Beta CDF and PDF for middle-sequencing models:  (conveyor system) ............... 144 Figure 3.30 Simulation results for the construction strategies:  side-sequencing (Scenario-ESH and Scenario-ESV) versus Middle-sequencing Case 1 (Scenario-EMH and Scenario-EMV) ... 146 Figure 3.31 Simulation results for the construction strategies:  side-sequencing (Scenario-ESH and Scenario-ESV) versus Middle-sequencing Case 2 (Scenario-EMH and Scenario-EMV) ... 147 Figure 4.1 Schematic diagrams of project percentage complete ................................................ 162 Figure 4.2 Schematic diagrams of project percentage remaining (aggregated remaining work) 162 Figure 4.3 Schematic diagrams of project earned value analysis ............................................... 164 Figure 4.4 Schematic diagrams of earned value ......................................................................... 165 Figure 4.5 Schematic diagrams of aggregated remaining work ................................................. 165 Figure 4.6 Aggregated remaining work and progress rates for three sample paths and planned path .............................................................................................................................................. 171 Figure 4.7 An example of a conditional expectation function at given time interval (plot for 1 time step) ..................................................................................................................................... 172 Figure 4.8 Planned schedule for development and construction work packages ....................... 178 Figure 4.9 Planned versus simulated evolution for three paths in the numerical example out of 10,000 sample trails (paths) ........................................................................................................ 180 Figure 4.10 Histogram of the budget, inclusive of contingency, for two work packages .......... 181 Figure 4.11 Beta distribution of the budget, inclusive of contingency, for two work packages 181 Figure 4.12 Work package parameter assignment matrix – Scenario-ESH ................................ 183 Figure 4.13 Work package parameter assignment matrix – Scenario-ESV ................................ 183 Figure 4.14 Work package parameter assignment matrix – Scenario-OSV ............................... 184 Figure 4.15 Work package parameter assignment matrix – Scenario-ELV (Case 2) ................. 184 xix  Figure 4.16 Trade-off analysis between computational time and number of simulation paths .. 187 Figure 4.17 Beta distributions for the four flexible scenarios .................................................... 188 Figure 4.18 Work package parameter assignment matrix for a construction project comprising multiple work packages .............................................................................................................. 190 Figure 4.19 Planned versus simulated evolution for three paths of aggregated remaining work for a project comprising eighteen work packages ............................................................................ 193 Figure 4.20 Cumulative capital expenditure for base case scenario for a project comprising eighteen work packages .............................................................................................................. 193 Figure 4.21 Histogram of the budget for the base case scenario for a project comprising eighteen work packages ............................................................................................................................. 194 Figure 4.22 Beta distribution of the budget for a construction project comprising eighteen work packages ...................................................................................................................................... 194 Figure 4.23 Beta distribution functions of the budget for five different delay levels ................. 197 Figure 4.24 Percentage contingency for five different confidence levels .................................. 197  xx  List of Symbols  A  Optimistic activity duration a  Pessimistic value corresponding beta distribution of delays AC  Actual cost B  Pessimistic activity duration b  Optimistic value corresponding beta distribution of delays C  Project cost base estimate c  Unit cost ct  Computational time sC  Calculated incurred project cost for given path D  Work Package duration d  Most likely value corresponding beta distribution of delays e  Euler’s number (mathematical constant) mE  Number of resources for activity or work package EV  Earned value f  Effort level value betaf  Beta distribution function calsf  Calculated effort level value for given path *sf  Optimized effort level value for given path xxi  trif  Triangular distribution function H  Number of paths i  Interval  j  Step sk  Calculated incurred project budget for given path *k  Optimized project cost L  Coefficient vector  M  Most likely activity duration m  Activity or work package  mP  Productivity of the work for activity or work package PV  Budgeted planned value for planned schedule mQ  Scope of work for activity or work package mq  Progress rate for activity or work package  sR  Remaining budget for given path S  Path T  Activity duration  t  Time (time step) mT  Activity or work package duration ( )au t  Project forecasted actual progress rate  ( )pu t  Project planned progress rate   xxii  RV  Variation in the expected budget  ctV  Variation in the computational time ( )pW t  Planned aggregated remaining work  ( )aW t  Forecasted actual aggregated remaining work  y   Regress vector  z  Regressor vector tz  Transpose of the regressor vector   Beta distribution shape parameter    Beta distribution shape parameter n  Random variable following Beta distribution   Weibull distribution shape parameter    Weibull distribution failure mode parameter  ( )p t  Planned percentage complete ( )a t  Actual percentage complete   Error vector  xxiii  List of Abbreviations  AUPC  Advance Undercut Progress Cycle CCM  Comprehensive Construction Model CDF  Cumulative Density Function  CDM  Comprehensive Development Model COA  Cyclic Operating Activity CTC  Conveyor Transfer Chamber  DB  Drawbell DES  Discrete Event Simulation  DOZ  Deep Ore Zone DP  Dynamic Programing  ENPV  Expected Net Present Value FCFS  First-come-first-served  FRC  Fiber Reinforcement Shotcrete  GBM  Geometric Brownian motion IDM  Initial Development Model KSM  Kerr Sulphurete Mitchell  LHD  Load Haul Dump LSM  Least-squares Monte Carlo ML  Most likely  MO  Monte Carlo MRMR Mining Rock Mass Rating  xxiv  MRP  Mean-reverting Process MTBF  Mean Time between Failures  MTBR  Mean Time between Repairs MTTR  Mean Time to Repair  NOA  Non-operating Activity NPV  Net Present Value OPT  Optimistic  OR  Operation Research  PDF  Probability Density Function PERT  Program Evaluation Review Technique  PES  Pessimistic RMR  Rock Mass Rating ROV  Real Options Valuation SCM  Scenario Construction Model SDM  Scenario Development Model TBF  Time between Failures  TCM  Typical Construction Model TDM  Typical Development Model TOR  Time-of-repair TTF  Time-to-failure TTR  Time to Repair  U/C  Undercut  xxv  Acknowledgements  I offer my enduring gratitude to the faculty, staff and my fellow students at UBC, who have inspired me to continue my work in this field. I owe particular thanks to Dr. W. Scott Dunbar for enlarging my vision of engineering and providing coherent answers to my endless questions. This thesis would not have been possible without his support, guidance and supervision. He gave me the opportunity to work with him as a lab instructor in the ore body modeling and simulation course. I thank Dr. Malcolm Scoble who provided an outstanding and thoughtful feedback to my work. He gave me the opportunity to work with him in the Cave Mining System course for 3 consecutive years.  He taught me how to design a project based leading course that engages both academics and industry. I thank Dr. Alan Russell whose penetrating questions taught me to question more deeply. He gave me the opportunity to work with him as a teaching assistant in the project and construction economics course for 4 consecutive years. I would like to acknowledge the research scholarship support provided by King Abdul Aziz University (KAU). I gratefully acknowledge the assistance of the New Afton mine, British Columbia, for collaboration on this research project work in providing the opportunity to study simulation and the nature of caving design issues in a characteristic underground setting. Special thanks are owed to my parents, who have supported me throughout my years of education, both morally and financially.  xxvi  Dedication  This thesis is dedicated to:  To my mother, Awatif, and father, Magdy, for their endless love. To my wife, Ghadeer, for her love, support and encouragement. To my sister, Walaa, and brothers, Wael, Hani, and Hossam. To my great son, Yassir, and lovely daughter, Jana. To all my family and friends.  1  Chapter 1: Introduction  1.1 Overview of the Future of Mass Mining Challenges  Owing to the increasing global demand for mineral resources, underground mass mining systems have recently gained significant attention of researchers and industry practitioners. The world copper usage has increased by more than 300% in the last 50 years while its global production has grown by an average of 3.2% per year, reaching 16.7 million tonnes in 2012, as shown in Figure 1.1, and reported by the international copper study group (ICSG, 2013). Currently, about 70% of the copper production comes from surface mining. Nevertheless, in 2013, it was posited that, compared to underground production, open pit production will decrease, since existing open pits are approaching their critical depth and more reserves are situated underground. As shown in Figure 1.2, by 2018, it is estimated that half of the cooper supply will be produced from underground mines (Moss, 2011).      Figure 1.1 World copper mine production from 1900 to 2012 (Source: International Copper Study Group, 2013) 2   Figure 1.2 Percentage of copper to concentrator by mining method from 2006 to 2018 (Source: Moss, 2011)  Cave mining systems are a highly promising underground mining methods, with the potential for exploiting deep, large and low-grade deposits at a relatively low cost and high productivity. Caving methods are primarily used for extracting copper-gold deposits and other associated minerals, e.g., silver, nickel and/or molybdenum. Well-known examples of existing caving operations include Palabora, Finsch, and Kimberley in South Africa, Northparks, Cadia east, and Argile in Australia, El Teniente, El Salvador and Andina in Chile, Deep ore zone (DOZ) in Indonesia, Henderson in USA, and New Afton in Canada. While there are several proposed caving operations—including Bingham Canyon and Resolution copper in USA, Chuquicamata in Chile, Oyu Tolgoi in Mongolia, Telfer and Mount Keith in Australia, and Grasberg in Indonesia—these projects are  presently in various phases of development and construction. In British Columbia, Canada, potential block caves are currently being planned, some of which could be standalone block caves. Locations of these initiatives are shown in Figure 1.3. 3   Figure 1.3 Current and future potential block cave mines in British Columbia, Canada (Source: Google Earth view)  The KSM project located in the Coast Mountains in northwestern British Columbia is another example of a cluster of four distinct gold-copper-silver deposits containing the Kerr, Sulphuretes, Mitchell, and Iron cap deposits (Tetra Tech, 2012). These small- to medium-sized deposits comprise relatively low-grade gold and copper minerals and are distributed over a very large area. The prefeasibility study for KSM project (Golder, 2012a, 2012b) indicated the feasibility of two block cave systems for Mitchell and Iron cap deposits. Presently, it is anticipated that the Mitchell deposit will be initially exploited as an open pit for approximately 26 years, before transferring to a block cave mine for another 27 years. On the other hand, the Iron cap deposit will be a standalone block cave, with the exploitation potential of 27 years as well.   4  The concept of using caving methods and new technology for the next generation “ore factory” prompts the need for applied research into tools to improve the reliability of underground cave mining design and planning (Moss, 2011). The “ore factory” draws parallels between cave mining systems and the approach adopted in the evolution of manufacturing engineering and management. The architecture of the factory represents long term infrastructure designed for the mine life, with the primary objectives of safety and financial security based on a reliable and consistent flow of ore that feeds an integrated mine to mill system. In order to serve this vision, several important levels in the lower part of the ore body need to be built including the development of: apex, undercut, extraction, haulage and ventilation drifts and raises, as shown in Figure 1.4.    Figure 1.4 Schematic diagram of an underground cave mining system, including the interconnected infrastructure levels at the bottom of the ore body   5  Projects of this nature require significant capital expenditure and long-term commitment of human and material resources before production commences. The development and construction of these systems might take several years and is thus a risky undertaking, given the highly uncertain environment and typical multibillion-dollar expenditures. Risks and uncertainties of caving are deemed higher than those associated with other mining methods, due to their complexity and the need to coordinate construction of all infrastructure components. Moreover, the scale of the underground operations and the sensitivity of effectively initiating the caving process, as shown in Figures 1.5 and 1.6, further contribute to the difficulties in planning and executing such projects. Thus, the main challenge is delivering the project within budget and on schedule.    Figure 1.5 Schematic 3-D diagram of an underground cave mining system, including the interconnected infrastructure levels as well as the drawbells (Moss, 2011) 6   Figure 1.6 Schematic 3-D diagram of an extraction level as associated drawbells (Moss, 2011)  1.2 Problems Related to Underground Development and Construction  Cave mining projects are confronted with numerous challenges in maintaining their construction schedule expectations. Deviation from forecasted schedule target values contributes to the wide range of uncertainties implicit in such projects. Uncertainty in construction productivity is attributed primarily to geotechnical and other equipment-related risk factors. Some of the issues can be eliminated through proper effective design and planning. However, geotechnical issues, in particular, cannot be fully eliminated since geotechnical data in mine development is inherently limited prior to construction (Kazakidis, 2001).    As a result, the mining industry has consistently failed to satisfy target development rate and construction dates for underground mining projects. In this context, development is referred to as the progression of sequential tunneling using drill-and-blast technique, while construction is 7  defined as the process of constructing drawbells (production cells) that connect the undercut and extraction levels. As highlighted by Moss (2009), sustaining development requirements is a critical measure of the success of a cave mining operation. A typical target of four meters advanced per drift per day is not unusual and can be achieved. However, increasing demand, combined with limited resources, has resulted in the need to increase the development rate to an average of eight meters per drift per day (Moss, 2009). This greater efficiency would reduce the development phase and thus provide safe access to construction team to build drawbells ahead of the initial schedule (Akerman & Parsons, 2014; Moss, 2009).   Normally, small caves consists of several thousands of meters of drifting and hundreds of drawpoints (e.g., New Afton mine requires development and construction of approximately 20 thousand meters of lateral headings and 378 of drawpoint respectively). However, construction of “super caves” (e.g., Oyu Tolgoi, Resolution or Chuquicamata copper mines) entails hundreds of thousands of meters of drifting and thousands of drawpoints. For an example, the total lateral development of Oyu Tolgoi mine exceeds 115 thousand meters with approximately 1690 drawpoints to be constructed. While such a significant undertaking is expected to be subject to some delays, these can have an enormous impact on the economic value of such projects. Any delay to construction of drawbells impacts on the production schedule and thus requires longer start-up production phase. This, in turn, reduces the project economic expectations. Delays can be attributed to many factors such as cave control, hangups, secondary blasting, ground and equipment related problems.     8  The standard scheduling processes of development and construction are not often designed with provisions for proactively managing uncertainties. Mine planners usually strive to design and plan cave systems that are reactive to construction risks. They often optimize the design and make the best decisions in the planning phase, aiming to build more reliable, safe, cost-effective mines based on the most likely scenarios. As a result, they tend to focus on minimizing the upfront cost of construction, rather than managing schedule delays by making greater initial expenditures to achieve the project schedule. This strategy is typically adopted, as less upfront capital required for construction makes projects more attractive to investors. Nevertheless, greater economic benefits can be achieved by bringing the project in on schedule.   1.3 Challenges to Introduce Flexibility during Construction  Once construction commences, there is very limited opportunity to change the cave mining system design. In the initial mine feasibility studies conducted during the design and planning phase, there is an opportunity to explore alternatives and assess risks. However, once construction starts and significant upfront capital is devoted to the construction of facilities, ventilation infrastructure and safe access to the ore body, then little can be done to develop significant design changes. At this point, a decision to change the mine design, operation plans, or even shut down the mine would have significant social, safety, technical and economic consequences.   This process inflexibility arises mainly from the fact that once caving has been initiated, it is difficult to change the design of the excavation infrastructure (e.g., extraction layout), or modify the strategy of undercut technique and sequencing. In particular, after the first drawbell has been 9  blasted, the design is practically irreversible, as effective cave initiation and propagation is the key element to successful mine life cave operation (Laubscher, 1994). Figure 1.7 illustrates that flexibility in long-term strategic decision-making process tends to diminish as the project matures, and is therefore replaced by short-term tactical operational decisions.     Figure 1.7 Strategic and tactical role in pre-production phase  1.4 Problems Related to Capital Budget Estimation  Mine planners and contractors also face challenges to deliver these complex projects within the assigned budget, making the financial estimates a very important aspect of such projects. Initial budgets are typically exceeded due to the practice of estimating cost contingency using subjective judgment as a fixed number or percentage addition to the base estimate. This approach is deemed unsatisfactory because it is arbitrary and difficult to justify (Idrus et al., 2010) and has low accuracy (Baccarini, 2004). Most financial forecasts in construction projects are based on 10  intuition, judgment, historical data, past experience, and rules of thumb (PMBOK® Guide, 2008). Yet this traditional method has been widely criticized, as it is believed to be the reason why many projects are completed over budget (Adfin et al., 2014; Bello and Odusami, 2008).   It is reasonable to assume that a better evaluation of budget, inclusive of contingency or risk mark-up, would result in more optimal project performance in terms of financial expenditure. A contractor’s budget typically includes indirect, direct, and overhead costs, as well as mark-up for risks and profit (Dikmen et al., 2007; Polat & Bingol, 2013). Here, cost contingency is typically added to the base budget to calculate the budget baseline. Determining the correct budget helps contractors achieve their cost objectives and target profit margin, whereas low or high cost contingencies may result in potential of project failure (Tseng et al., 2009; Polat & Bingol, 2013). Thus, an approach to identifying and incorporate sources of project delays and cost variability in development and construction, while simultaneously incorporating construction decision-making strategies into the valuation process of estimating project cost contingency, could be a key element to successful project delivery from contactor’s perspective.   1.5 Research Motivation  The motivation for this research was that accelerating the pre-production phase through strategic flexibilities can provide a significant increase in the expected economic value of such a mining project. Here, it is posited that shifting production inflows earlier in the project’s cash flow can truly increase the expected net present value (NPV). The problem, however, is identifying the construction strategies that can be employed to meet such objectives, where the chosen strategy would be incorporated. Further challenges include determining how a chosen strategy would be 11  practically integrated with respect to design constraints, mine schedule, and cost structure. This strategy is referred to as “strategic flexibility,” “flexible strategy” or simply “flexibility.”   The wide range of impediments to the timely completion of construction processes and poor ground conditions often encountered in mining projects are the main causes of excessive delays. This should be a strong incentive for seeking flexibility and identifying strategies that can improve construction performance. In this study, it is hypothesized that this can be achieved by prioritizing the construction schedule or changing the construction strategy, so that a wider range of options can be exercised (e.g., the crash option). The ability to exercise construction acceleration is critical for project managers to proactively adapt to geotechnical and technical (e.g., underground equipment-related) uncertainty that can delay some critical activities.   Accelerating (crashing) an activity or schedule requires a method or technique that can shorten the process duration without compromising safety and quality. In practice, however, it typically involves making schedule and cost trade-offs by optimizing between schedule duration reduction and cost increment (PMBOK® Guide, 2008). Crashing can be exercised to proactively manage the possibility of changes in the circumstances of the rock mass and the construction productivity, such as reduction in equipment utilization, shortage of resources, equipment breakdowns, and scheduling issues that can lead to schedule delays.  Although several ways to crash activities exist, the most common ones rely on providing additional resources, using overtime and multiple shifts, as well as changing the construction method and technology. In caving projects, however, it is not possible to increase performance by introducing overtime, since it is typical in mining construction for crews to work in two 12-12  hour shifts. In addition, at this time of the study, the drill-and-blast method is common practice in underground development. Therefore, the only project crashing method investigated herein is one based on increased equipment utilization.    The geological and geotechnical characteristics of a cave mining project significantly affect the design of excavation system and sequence, for example, the undercut starting point, face orientation, sequencing strategy, as well as the extraction layout design and drawpoint spacing. These factors are critical for proper cave initiation and propagation and thus construction crashing by improving resource utilization is sometimes difficult to implement in narrow deposits unless a flexible strategy is implemented so as to relax the spatial constraints imposed by this mining method. Those strategies must be adopted in the design and planning of cave systems, in which integration of the option of construction acceleration can be incorporated and thus exercised without difficulty.  Review of available literature on mining planning and design revealed limited studies that provide systematic and formal review of available methods for modeling flexibility. In particular, very little work has been conducted on caving and, specifically, the construction phase. Most of the research efforts are usually dedicated to operational flexibilities, those inherent in the production phase. With respect to pre-production phase, most of the works on cave mining systems focus on verifying the development plans, examining optimized mine design, or allocating development and production resources. Such studies have demonstrated the ability of simulation tools to model caving systems and aid mine planners in developing a base case design and schedule. However, further attention is still required to develop technical models that 13  examine different flexible scenarios related to construction. Similarly, additional studies are needed for developing pricing models that can estimate the budget, inclusive of the cost of implementing crashing options. Empirical evidence suggests that the tendency to ignore the decision-making process in the contractor’s budget estimation may result in an increased discrepancy between the estimated and actual cost. Thus, these issues will be explored in this study, with more details provided in Chapter 2, 3 and 4.  1.6 Research Questions   This study seeks to expand the current knowledge on three interrelated domains of engineering systems—(1) recognition, (2) modeling and (3) pricing of flexibility in underground cave mining construction. Cave mining system planning and design is illustrated in Figure 1.8. This research fits into details mine design and planning, specifically in development and construction planning as shown in Figure 1.8. An objective of this study is to provide state-of-the-art techniques and tools employed in planning that can be used to support decision-making processes in cave mining systems. This first domain requires identifying presently utilized construction strategies that allow the mine management to implement construction crashing in the multiple face heading. The second domain is achieved by investigating and evaluating the development and construction rates enabling implementation of those flexible strategies and thus increasing construction performance. The third domain requires development of a methodology suitable for evaluating the cost of the implementing construction crashing option that can accommodate delays. Crashing options in project scheduling refer to the premium cost needed to have the option to execute a task by reducing execution times to meet project schedule targets.  14   Figure 1.8 Process diagram for cave mining systems planning and design    15  This research is driven by the following research questions:   1. Is it possible to incorporate strategic flexibilities into the development and construction of cave mining systems in order to facilitate the exercising of crashing option (construction acceleration) and thus improve the rate of development and construction productivity?  2. How can the power of simulation techniques be utilized to emulate the actual process of an existing case study and subsequently model and examine different scenarios with respect to those identified flexible scenarios to aid the analysis of development and construction performance? 3. What method can be developed to explicitly incorporate the cost of the decisions made by the construction project manager at project milestones to crash activities or work packages to proactively manage schedule-related uncertainties and, consequently, estimate the budget, inclusive of cost contingency?  1.7 Research Objectives   The main objectives of this research are to: 1. Identify and discuss three independent and interrelated flexibilities in the interconnected horizontal infrastructure levels within the ore body footprint, apex, undercut, extraction, and haulage level, in which construction crashing by improving equipment utilization can be exercised.   2. Develop and describe a process capable of modeling the development and construction processes with respect to the advance undercut strategy, which integrates the geotechnical and technical uncertainties, using the framework of discrete event simulation (DES), and 16  thus investigate and examine the enhancement of construction productivity compared to a conventional construction strategy.    3. Develop and describe a methodology that is able to respond to schedule uncertainties in construction projects by incorporating the decision-making strategy of project crashing into the budget, including the cost contingency valuation, using the framework of real options and Monte Carlo simulation from a contractor’s perspective.   1.8 Research Contributions   The main contributions of this study stem from its ability to: 1. Formally discuss the design considerations and planning aspects for flexibility in construction with respect to the three critical levels of cave mining system—haulage, extraction, and undercut levels. 2. Develop a method based on the Discrete Event Simulation (DES) methodology that can model the process of development and construction in each advance undercut progress cycle likely to be executed in construction of small block cave systems, in which multiple face heading can be conducted simultaneously in the interrelated levels—apex, undercut, and extraction, and thus investigate and examine the enhancement of construction productivity using the results obtained from the DES models. 3. Develop an algorithm that can estimate and allocate cost contingency over project work packages in order to pay for not extending the schedule (i.e., to avoid delays). A stochastic process was developed that can be integrated into a framework of simulations that implicitly account for sources of schedule uncertainties and risk events for projects in overlapping work packages.  17  1.9 The Case Study: New Afton Mine 1.9.1 Overview  New Afton is an underground block cave mine located approximately 8 km west of the city of Kamloops, British Columbia. The underground low-grade copper-gold deposit lies beneath an existing open pit contains reserves of 1 million ounces of gold and 1 billion pounds of copper. This reserve estimated at approximately 52 Mt contains an average of 0.65 g/t gold and 0.93% copper. It is expected to have 12 years of mine life at an annual production of 4 million tonnes per year, or 11,000 tonnes per day (Prince et al., 2013). The foot print is located approximately 0.5 km below surface and has 85 thousand square meters.  New Afton is chosen as the case study in this research for many reasons. First, the research will be based on a mine whose management has constantly sought state-of-the art techniques and tools, and conducts due diligence in all aspects of safety and production. For example, a fire detection system along the length of the decline and conveyor belt has been installed with automatic sprayers installed at certain locations. Second, the mine management is very generous with help and assistance to researchers and students from the University of British Columbia, Vancouver. Third, the mine is located in British Columbia, where conducting several site visits to the mine and exploring characteristics of development and construction is not challenging.   However, the main reason for choosing the mine is that the present study commenced at the time when the mining team had just completed the main access and conveyor drifts. Thus, it had started development within the ore body, where most horizontal infrastructures are located, including apex, undercut, extraction, and haulage levels. In addition, the mine is relatively small, 18  compared to other mines; thus, construction and development of different phase milestones can be observed in a shorter amount of time and match the schedule and scope of this research. Despite significant complexity of the structural geology of the deposit, five prominent major faults affected the mine design—Hanging wall, Footwall, North-East, North-West, and North faults (Hatch, 2007). The ore body is bounded by two weak faults—the Hanging wall from the south side and the Footwall from the north side—where most of the existing infrastructure is located, as shown in Figures 1.9 and 1.10. This results in very weak Rock Mass Rating (RMR), ranging from RMR 35 to RMR 50—in weak ground conditions. The footprint of the main horizontal infrastructure is located approximately 600 m below the surface. With large, deep, and low-grade ore deposits, in which operating cost is a significant factor and weaker ground conditions can promote caveability, selection of this mining method is not unusual.    Figure 1.9 North-west cross Section of the main infrastructure and geological features of New Afton mine (Source: New Afton mine, 2012)N18   Figure 1.10 Isometric view of New Afton underground mine infrastructure (Source: New Afton mine, 2012)19  1.9.2 Development and Construction Process Construction of block caving in New Afton and other similar sites involves three major steps, shown in Figures 1.11 and 1.12. These comprise the development of (1) vertical access to the underground footprint (primary access) and (2) horizontal drifts and vertical raises required to arrive at the ore body (secondary access); as well as (3) development and construction of extraction, undercut, and other infrastructure levels within the ore body (tertiary access). The development process must precede the construction process, as lateral tunneling is necessary to provide access to construction crews to build drawbells that connect the undercut and extraction levels.    Figure 1.11 Schematic diagram of the three phases of the development and construction20   Figure 1.12 Plan view of New Afton infrastructure completed during construction phase (Source: New Afton mine, 2012)21  The construction and development of a typical underground block cave mine starts with a vertical development that extends to the bottom of the ore body where most of the lateral infrastructure is located. The manner in which the vertical infrastructure is constructed varies between mine designs. The approach adopted in the current case study requires use of the main access and conveyer declines and ventilation raises, as shown in Figure 1.10. Depending on the production target, the decision regarding the vertical system requirements must be undertaken in the design and planning phase and depends on many factors, including the production target, depth and size of the ore body, and most importantly the cost of vertical development.  Upon arrival at the footprint level, the second stage commences with the development of major drifts and raises connecting the vertical system to the ore body. This stage also involves initial construction of the conveyer belt, as a part of the ore handling system, as well as underground facilities such as refuge stations, storage rooms, fuel stations, explosive magazines, and lunch rooms. Ventilation capacity will be increased at this stage to suit the needs of the next phase of lateral development and support the subsequent start of the operation phase. In New Afton, a footwall drive is used to link the access drifts and facilities to those production levels in the footprint. This approach is necessary, as the vertical system has to be far away from the subsidence zone due to caving that occurs within the ore body footprint. In New Afton, the footwall drive is located in a very weak fault, the footwall fault, and required intensive ground support since it is the main access to the apex, undercut, and extraction levels.  The last stage consists of the development and construction of the apex, undercut and extraction levels at the bottom of the ore body. This stage requires significant capital and time commitment. 22  Finally, the extraction level with all drawpoints is built and the ore handling system is completed. The ore handling system consisting of a permanent crusher complex, ore passes, haulage drifts, and conveyor station is intended to be fully utilized during production. It also involves construction of roadways and a ventilation system. As this phase is characterized by multiple face headings, close attention to resource utilization is critical (Moss, 2009).  1.9.3 Uncertainty in the Construction  Uncertainties in the outcome of construction performance are assumed to have significant negative effect on the overall progress of the mining project, as they typically result in costly delays in some major activities. In order to avoid any unforeseen issues, design and planning is conducted. However, these measures are often undertaken based on the results obtained from a few hundred bores, which is not exactly representative of the entire ground conditions. Yet, despite having very limited information at their disposal, mining team is required to provide mine design criteria, a construction schedule, and a production plan. Moreover, construction and development are extremely equipment intensive processes in highly uncertain underground conditions and thus major breakdowns are expected.   In this study, two major sources of uncertainties that contribute to construction delays will be investigated:   1. Encountered rock mass variability; and  2. Mining equipment utilization variability   23  1.10 Thesis Structure This thesis consists of five chapters. Chapter 1, the current chapter, introduces the topic of planning for flexibility in the construction of the underground cave mining systems. It provides an overview of the future of caving mining initiatives, which rely on mass mining systems. It also highlights the causes of delays faced by the development and construction teams, and the challenges to introducing flexibility during construction. Research motivation, objectives, and contributions are also outlined. A representative case study is introduced to demonstrate the applicability of the concepts used.   Chapter 2 discusses three sources of flexibility that can be integrated into the planning and design philosophy. Since any complex system can be studied by dividing its structure into smaller components or sub-systems, this approach will be adopted here. This segmentation allows focusing on both independent aspects of the sub-system and the interdependent elements linking those sub-systems together. More specifically, the caving system studied here is divided into three sub-systems—ore handling, extraction, and undercut sub-systems—and planning and design aspects for flexibility are subsequently discussed. Chapter 3 describes modeling and evaluation of those flexibilities. Scope of modeling and model evolution, development, and uncertainties are covered, as well as simulation scenarios and results. Using the DES model described in Chapter 3, Chapter 4 discusses the development of a method based on least-squares Monte Carlo (LSM) that can estimate the budget, inclusive of cost constancy in capital project. Results are demonstrated for the same modeling scenarios used in Chapter 3. Finally, Chapter 5 draws conclusions based on the DES (Chapter 3) and LSM (Chapter 4) results. Recommendations are made for possible future work to improve the methods developed. 24  Chapter 2: Recognition of Flexibility in Cave Mining Design and Construction  2.1 Introduction This chapter deals with a fundamental issue in planning and design: recognition of flexibility in development and construction of caving systems. The main contribution of this chapter is discuss the key design considerations and planning aspects required to introduce  flexibility into the  construction of cave mining system. Flexibility recognition in development and construction of cave mining systems refers to the realization of strategies that can be adopted in the design and planning of cave systems, in which integration of construction acceleration can be incorporated and, thus, exercised without difficulty.  Mayer and Kazakidis (2007) indicated that formalizing possible flexible alternatives is a milestone step in planning for flexibility in mine production systems.  It involves determining the condition in which it becomes worth executing and the cost associated with it to make it available.  In what follows, more emphasis is placed on framing potential flexible design and planning options than on screening for all options availability.    Building flexibilities in cave mining system planning and design not only will control the negative dimension of uncertainties, but will also enhance the project economic value. Flexibility is defined herein as the ability to utilize multiple sub-systems simultaneously, execute an alternative construction strategy, or switch from one design choice to another to proactively deal with uncertainty, and results in improving construction performance targets.  It is essential to treat uncertainty as the fundamental (time-cost) element of system design, planning, and management (De Neufville et al., 2004). Uncertainty normally refers to probability for positive or negative consequences.  However, in construction, the focus tends to be on the negative side 25  of the probability distribution that brings delays to construction performance.  Geotechnical and equipment-related problems are considered significant sources of internal risks in most underground mining projects, and contribute to project delays and associated cost overruns.   Three strategic flexibilities are considered herein.  Each one is related to a specific sub-system (e.g., undercut, extraction, or haulage level). Despite the interdependency between the horizontal infrastructures levels connected at the bottom of ore body and depending on the design of the mine, each option can be exercised separately or combined with the other options as a compound option.  The ultimate goal is to find flexible ways to implement crashing options by relaxing the underground-related constraints.   The three crashing options are as follows: 1. The ability to implement a crashing option by utilizing the ore handling system early in the construction phase and, thus, improving mucking strategies in the process of development and construction;  2. The ability to implement a crashing option by changing the extraction layout from Offset Herringbone to El Teniente layout and, thus, improving equipment utilization and accelerating the construction phase; or 3. The ability to implement a crashing option by changing the undercut sequencing strategy from side to middle sequencing and thus increase the number of machines utilized.    26  2.2 Literature Review This literature review section is structured to cover three interrelated domains of engineering system planning and design:  flexibility, uncertainty, and real options. First, flexibility is described from a conceptual point of view, beginning with the definition used by researchers in the field of mining and engineering systems. Then the topic of uncertainty and risk is covered. Flexibility and real options are linked together to complete the picture and establish a common ground on which to discuss the context of flexibility in the development and construction of caving mining systems.    2.2.1 The Context of Flexibility in the Decision-Making Process  In broad terms, flexibility is the ability to adapt a system to cope with variability and uncertainty. In engineering design and operation, it is the capability of the system to react to negative conditions and to take advantage of positive opportunities. The concept of flexibility emerged in the early 1980’s in the manufacturing industry and then subsequently emerged into mining engineering.  In mining projects, it governs the capability of the mining company or project to respond to change (Dunbar et al., 1998).  Mayer and Kazakidis (2007) define flexibility as “the ability to sustain performance, maintain cost structure, adapt to operating risks, and take advantage of new opportunities.”  Different levels of managing decisions are frequently appropriate for different phases of cave mining projects. Three levels of decision making are common for those projects:  strategic, tactical, and operational decisions. In contrast to operational decisions, which are made daily, strategic decisions are future-oriented, typically in years for block or panel cave projects.  Long-27  term decisions are concerned with the approaches that directly relate to business objectives and design requirements. As discussed by Newman et al. (2010), how to position underground facilities, how to extract the mineral reserve given the ore geometry are strategic decisions as part of the mine design requirement. Tactical decisions, however, are shorter-term, and normally relate to implementing preceding strategic decisions.  They are phase-specific and normally occur within the phase in progress, typically in months for such projects. Mine sequencing, production scheduling, and equipment selection are usually considered tactical decisions (Newman el al. 2010).   Strategic flexibility in cave mining systems is considered strategic decision-making in which design, planning, and cost implications should occur in the planning phase, ideally, a few years before production commences.  The term “flexibility” will be used herein to represent “strategic flexibility” unless the author explicitly states “tactical flexibility.” Generally, more freedom to test different strategic scenarios and identify and evaluate several risks are available in the planning phases.  Alternatives to management operations tend to diminish exponentially as the mine matures (Kazakidis & Scoble, 2003). Planning and design occurs in the front-end phase, before making the decision to proceed with the execution phase. Strategic planning is concerned here with the stage which ranges from the conceptual to detailed feasibility studies.  Keer (2004) discusses the conceptual, pre-feasibility, and detailed feasibility studies as part of any mining project life cycle.    28  2.2.2 Flexibility within the Perspective of Real Options  The term “real options” was coined by Steward Myers in 1977, with “real” referring to real or tangible assets.  Wang (2005) discussed the history of real options. Basic concepts of real options and option pricing are available extensively in the literature (Dixit & Pindyck, 1994; Trigeorgis, 1996; Amran & Kulatilaka, 1999; Copeland & Antikarov, 2001; Mun, 2006).  An option is defined as the right, but not obligation, to undertake certain business initiatives under predefined arrangements (De Neufville et al., 2004).  It is not equivalent to alternative or a choice.  Fundamentally, the distinction is that there is cost associated with using one’s right to undertake a defined action and exercising the option has value (De Neufville, 2003).  Real options is the building block to formally define flexibility (Wang & De Neufville, 2006). The most common examples that can provide operating flexibility and strategic adaptability are discussed by Trigeorgis (1996). Examples of real options examples are the deferral, abandon, expansion, and shut down options.   Real options differ from financial options, as real options deals with real assets (physical assets), rather than financial contracts. A financial option are restricted to buying or selling an underlying asset, typically called “call” or “put” options, not as in the case of real options where it has to do something for a certain cost within a specific period of time (Wang, 2005). Many authors discussed the differences in implementing real options as opposed to financial options. One key difference in terms of engineering systems is that data on volatilities of real assets does not exist similar to those financial options (e.g., commodity and stock prices) and speculative assumptions are requested (Wang, 2005).  More often, there is no menu or list of potential candidates for real options to choose from as in the case of financial options. Risks in financial options are well 29  defined and a great deal of precision can be achieved. However, in real options, managers tend to find choices and compare alternatives with respect to relative values rather than specific values (De Neufville, 2003).   In an engineering system, emphasis is placed on real options “in” a project rather than “on” a project.  The distinction between real options in and on projects is discussed in De Neufville et al. (2004). Detailed comparison between them is found in (Wang and De Neufville 2005).  Real options “on” project concerns with the project itself and treat technology and system as a black box.  It is considered as a financial option taken on the technical aspects of the project.  They are investment opportunities and relatively easy to define compared to real options “in” a project where each option highly depends on the variable and parameters on the system component (Wang & De Neufville, 2005).  Most common types of options “on” projects are options to defer, to default (abandon for salvage), to expand, to contract, to shut down or restart, and to switch use (Trigeorgis, 1993).  Yet, real options “in” a project are concerned with the technical design elements of the system.  As real options “in” a project or system require a profound understanding about the system, options are created by changing the design elements of the system and considered to be design of flexibility in the system (Wang, 2005; Wang & De Neufville, 2005).  Creating flexibility in design is equivalent to creating real options (Nembhard and Aktan, 2009). Real options is the basic component that constitutes the definition and description of flexibility in a formal way (Wang and De Neufville, 2005; Wang and De Neufville 2006).  Likewise, the adaptability to construction uncertainty by minimizing the delays and improving the progress is 30  not obligatory but a right to execute decisions for a cost within specific timeframe. Flexibility in cave mining systems clearly can fit into the context and concepts of real options in projects.   2.2.3 Uncertainty and Risk in Mining  Much of the effort in surface and underground mine planning focuses on the uncertainty in production scheduling and treats the pre-production phase only with respect to market risks related to increase in capital or investment (Lemelin et al. ,2007; Groeneveld et al., 2012). Uncertainties can influence the decision-making process as internal and external uncertainties are realized (Mayer & Kazakidis, 2007; Kazakidis & Scoble, 2003; Dunbar et al., 1998). Mining project typically include market and non-market risks which are frequently referred to as internal (indigenous) and external (exogenous) uncertainties.  Internal uncertainties in underground mining operations are those that are dictated by the deposit itself (Kazakidis & Scoble, 2003). They can be classified as ground condition, equipment, grade distribution or recovery method uncertainties as well as labour force work disruption or social turbulences.  External uncertainties, however, can be in the form of market price, legislation, government policy, country risks, community development, or industrial relations (Kazakidis & Scoble, 2003).   Despite the fact that surface and underground mining share similarities as being risky environment due to uncertainty in equipment utilization, geotechnical problems in underground mines play significant role to uncertainty in contrast to surface mining.  Several studies indicated that operating risks in underground mines are a combination of equipment, schedule, and ground related risks (e.g Vayenas et al., 2003; Groeneveld et al., 2012). As discussed by Kenzap & Kazakidis (2013), those factors cause delays in production activities and consequently deviate 31  production gains from target revenue expectations. Risk related to equipment damage, infrastructure damage (e.g., stope or shaft damage), production loss, and other technical factors can significantly impact both revenue and costs, and lead to substantial delays.  In contrast, an open pit as surface mine is highly dependent on equipment and thus more emphasis has to be put on equipment reliability and less on ground-related problems.  2.2.4 Geotechnical and Technical Risks in Underground Mining  Geotechnical-related problems are significant sources of operation internal risks in underground hard rock mining (Kazakidis & Scoble, 2002).  They result in delays, cost overruns, and economic loss. Despite the rock engineering effort to minimize their impact by improving the designs and optimize the plans of underground mining support, they are inevitable and require proper consideration by developing systematic approaches to quantify the impact of ground related problems in the production performance. Kazakidis and Scoble (2002) developed a model that accounts for quantifying the impact of ground-related risks in underground mine production planning systems. They focus on the negative economics of ground-related problems due to operation delays.  Operation delays are caused mainly by deterioration of in situ geotechnical conditions and falls of grounds, which in turn lead to redesign, support, and rehabilitation. They classified various types of potential risks in underground hard rock mining and assigned relevant problems to the five different mine subsystems of, (1) store, (2) drift, (3) pass, (4) vent raise and (5) shaft, based on the special characteristics of each subsystem. Most of the risks identified can be categorized into in situ stress, blasting, groundwater, seismicity-induced damages, and causes of rehabilitation.  Those damages impose dilution and impact production quality. Mostly delays are attributed to rehabilitation.   32  With respect to machinery in mining, Vayenas et al. (1997) propose a methodology based on statistical analysis and reliability theory to account for equipment related problems.  As technology is developed to promote high mining productivity, equipment becomes more powerful and complicated and thus requires proper analysis with respect to failure and maintenance.  Quantifying and analyzing equipment downtimes based on mean time between failures (MTBF), mean time to repair (MTTR), and equipment availability depends on the availability and analysis of raw data. For an example, classification of equipment failure types encountered in a Load-Haul Dump (LHD) can be related be drive train (e.g., transmission or drivelines), hydraulic system, structure (e.g., frame, seat or canopy), breaking system, electrical system, tires, etc. Vayenas et al. (2003) used the same concepts of maintenance reliability of equipment and apply it to excavations and geotechnical problems.  2.2.5 Flexibility in Mining Engineering Systems Most of the flexibility introduced in mining projects is production-oriented. Flexible manufacturing systems share similarities with flexible production mining systems, in that both generally focus on increasing productivity, improving equipment utilization, and lowering operating cost.  Kazakidis (2001) studied production flexibilities with respect to geotechnical risks in underground mining. Kazakids & Scoble (2003) introduced four options in the design that can react to geotechnical (technical) risks in the production phase, have a second crusher, increase hoisting capacity at a later stage of the mine life, add an additional vent raise, or have a second ore pass.   33  Mine management makes use of best practices to focus on avoiding negative risks.  Positive risks, however, are often not fully recognized by mine managers, so those opportunities might be lost if not taken advantage of at the right time (Kazakidis & Mayer 2010).  Appreciating the risks and uncertainties inherent in operations is the first step toward achieving a business goal, followed by the management of identified flexibility. Types and examples of mining flexibility are discussed for example by Dunbar et al. (1998). Treatment of tactical flexibility as it is related to a distinct mining system requires different management than the strategic flexibility arising from several mine production operations. The ability to change the production rate to respond to metal prices, to advance mine development to cope with the reduction in stope development, to increase the exploration and delineation effort to minimize risks in ore body quality are examples of tactical flexibility.   Valuation of flexibility as integral parts of mine planning and design is crucial to success. Real options valuation (ROV) techniques provide meaningful systematic ways to cope with operation risks and to take advantage of the value surrounding uncertainties (Kazakidis & Scoble, 2003).  Where flexibility is integrated into the mine plan to mitigate operational risks, a flexibility index is introduced by Kazakidis & Scoble (2003) which assesses the most valuable flexibility alternatives in mine operations chosen from several alternatives.  This index captures the value of the flexibility with respect to the associated increased cost in capital and operation to the estimated value of the mine. The higher the value of the flexibility index, the greater the chances that this flexibility will increase the value of the mine. The ability to expand the mine production and the ability to incorporate the up-front modifications to design parameters are a sort of flexibility valued to cope with ground-related problems and stopping production variations.  34  Mayer and Kazakidis (2007) used a simplified Monte Carlo (MC) simulation in a spread sheet to value strategic options. Modeling of the sequential decision option, the shutdown option and the capacity option occurred by modeling the project investment costs and revenue generated by the project using Geometric Brownian motion (GBM) and then valuing this asset under different volatility measures. One important factor, which is always problematic, is the volatility estimate (Nembhard & Aktan, 2009). It requires management to analyze operating data records for each mine process not just quantifying project risks into one lumped volatility measure to account for all operating risks.   Despite the fact that a significant amount of work has been published on the application of real options valuation (ROV) in natural resource investment and specifically in mining industry valuation under uncertainty, it is still unclear whether the ROA can be applied practically in the mining industry and how it may improve the decision making process (Dimitrakopoulos & Abdel Sabour, 2007). These uncertainties are due to the difficulty in incorporating multi-dimensional sources of flexibility into the common real options techniques.  Fortunately, there are ways to overcome this problem by collapsing several sources of uncertainty into one factor, utilizing simulations, or even considering one significant factor of uncertainty in such models.  With respect to market uncertainty as metal price for example, several studies (e.g. Cortazar et al., 2001; Cardin et al., 2008) develop models based on a one-dimensional source of uncertainty.   Cortazar et al. (2001) developed a real options model for valuing natural resource exploration projects. Several options are considered in three phases of a mine plan.  An abandon option and an option of stopping/resuming operations were used in the exploration and operation phases 35  while a deferral option was the option used in the investment phase.  Those phases are optimized contingent to price and geotechnical-technical risks which are dependent on the expected final reserve. Decisions to exercise those options are based on cash flow expectations of different mine plans for different levels on mine reserves. These options are not “in” the project.  Those are investment decision options and for a large scale mine, it is practically infeasible to stop and resume mining based on the fluctuation of metal prices.    Cardin et al. (2008) proposed a general evaluation methodology that takes advantage of mining operating flexibility to increase the mine value. Management chooses to alter operations with respect to price risks only. The concept of a mine catalogue is introduced as management has three different mine operation plans and the selection of each plan depends on the price scenario used.  The first step in this process is defining representative uncertain scenarios.  The stochastic price process uses GBM is used to simulate future price scenarios. The second step is identifying the main sources of flexibility in mine operation. In open pit mining, for example, the size of the crushing mill can be changed and the size of the truck fleet can be modified and so on. Moreover, the flexibility to expand the mine plan or to shrink production can be exploited. The third step is to establish the mine catalogue, as the author used three mine plans to cope with positive and projected negative price changes. The last step is assessing the value of the flexibility added to the project of given price scenarios and the ability to switch between mine plans to create an optimal operating strategy for the particular mine infrastructure.  Although there is no doubt that flexibility will add value to mining projects, the actual percent added by introducing flexibility and the applicability to switch plans is questionable in many underground 36  mine cases when multi-dimensional sources of uncertainties exist, sources of flexibility are limited, and management is committed to certain plans.   Other ways to incorporate multiple uncertainties and non-uniformity of cash flow components is by simulating multiple realizations of the uncertain variables and making optimal decisions at each period using value expectation as outlined by Dimitrakopoulos and Abdel Sabour (2007)   who carry out a dynamic optimization process after simulation of several realizations of metal price, foreign exchange rate, and ore body models. This simulation-based real option approach attempted to outline a practical methodology to overcome the simplified methodology of using the one-factor GBM model. Although this approach is implemented on a small scale open pit gold mine in Australia in which gold price volatility is modeled stochastically as GBM, and foreign exchange volatility is described as mean-reverting process (MRP) and special variability of geological variable (e.g., ore grade and tonnage) is modeled using "conditional simulation" method, only one type of operating flexibility is considered, the option to continue or abandon the mine.  More effort is needed to cover the area with respect to the identification and recognition of real options in mining systems. Miller and Lessard (2001) argued that recognizing, creating, shaping, and realizing those options in large scale engineering projects is often required to win the battle against risks involved. They discussed the nature of risk in projects and offered ways to proactively manage those risks in large engineering projects. The authors suggested using the managerial approach of realizing that interactions among those exogenous risks and shaping of risk drivers should be part of the risk management process rather than just pricing the risks 37  involved. It reinforces the importance of framing flexibility and the real options model along with valuing risks using real options techniques. To identify real options in projects a deep understanding of system technology is required (Wang & De Neufville, 2005) so one can create an option in system planning and design.  2.2.6 Summary  Conclusions with regard to the conducted literature review is outlined below:  Research efforts in mining for flexibility are given to real options valuation techniques and methods of valuation and limited work is concentrated on recognizing, identifying, shaping, and framing real options that can practically add real economic values. Proper option framing is the first step toward proper modeling and evaluation.   Research efforts in mining engineering are usually put into operational flexibilities, those flexibilities inherent in the production phase where the mine is already built. Mostly they treat the construction phase as if it is merely a capital cost that experiences overruns. This is because not all mining methods require a long-lead pre-production phase, as in the case of caving systems. More focus in flexibility in development and construction of block caving is needed.  Most of the work in caving systems focuses on the uncertainty in production scheduling and little attention is given to construction. No method or tool used for production planning that can account for uncertainty in the complex geotechnical behavior of rock mass was available until Rubio (2006) developed a methodology based on reliability theory to account for production scheduling uncertainty. 38   In terms of geotechnical and technical uncertainties as part of project internal risks, there is a need to create technical models in a practical manner to examine the impact of those factors on the construction performance of block cave underground mining.   The development construction process of cave mining exhibits some similarities to underground mine production in terms of ground and equipment-related risks, as they are the major forces of internal risks that cause problems for project performance. Several authors argue that technical (e.g., equipment) and geotechnical (e.g., rock mass) problems are important keys to consider in any underground mining.   It appears that no systematic and formal method is available in the literature for introducing strategic and tactical flexibility in mining planning and design with respect to block caving and, in particular, to the construction phase.    2.3 Flexibility in the Ore Handling System The ore handling system is concerned with transporting the ore from the production level (extraction level) beneath the cave zone and then all the way to the surface. The haulage level encompasses most of the production ore handling system in which caved material moves from the undercut level through drawbells to drawpoints, as shown in Figure 2.1. Then, ore is transported by a fleet of LHDs from draw points at the extraction level and dumped to ore passes to be collected and trucked from the haulage level located underneath the extraction level.  Then, ore is transported and feed into a central crushing station from which rock material is sized and conveyed to the surface through conveyer drifts.39   Figure 2.1 Plan view of the New Afton haulage level including crusher complex and conveyor chamber (black circle) (Source: New Afton mine 2012)N 40  This system is often planned to be used in the production phase to serve the vision of the ore factory and, thus, the system components are scheduled to be fully built, installed, and commissioned in the production start-up phase and not often intended to be utilized in the early stages of construction. The instinct is always to shift the cost of building the ore handling facilities to the backend of this phase or balance the expenditure until revenue is gained from extracted ore. In that sense, this system is traditionally arranged to be fully utilized in the production phase.    Traditionally, upon completion of the vertical system and once lateral development starts on undercut and extraction levels, construction of the haulage level tends to follow the construction of the extraction level. It involves development of drifts below the extraction level and connecting both levels with ore passes and vent raises.  A central crusher station is connected to haulage drifts in which a large opening is required to suit the crusher chamber.  Timing of expenditures in that regard is optimized and distributed over the entire pre-production phase. Thus, as with traditional planning, the conveyer and crusher stations are only available during the production phase and cannot be utilized during the pre-production phase.   2.3.1 The Challenges Faced During the Pre-Production Phase  Development and construction of permanent and temporary drifts and drawbells require mucking of extensive amounts of material from the footprint to the surface.  For example, construction of a single drawbell in the New Afton mine requires an average of 5400 tonnes to be removed and transported by trucks to the surface using the access decline. This involves 10 days of mucking 41  activity using the truck hauling system. Moreover, each cycle of drifting (development activities) requires from 140 to170 tonnes of material to be transported.    This problem becomes more complicated in the development of multiple face headings and construction of drawbells, in which muck material must be hauled to the surface using trucks.  In some cases, there are approximately 25 open faces (e.g. six apex drives, five undercut drives, six extraction drives, five crosscut drifts) and all of them are advancing simultaneously. If the mine chooses a typical truck and hauling system (truck-haul) to transport all muck material to the surface, a large fleet of trucks and LHDs must be in place.    In the case of the New Afton mine, the early stages of construction focus on building the conveyer drift, decline drift and ventilation raises.  Upon reaching the footprint, attention is given to developing horizontal drifts that arrive to the production level in a short amount of time. Even within the footprint development, more attention is given to the development in the apex, extraction and undercut level rather than haulage ones. At that time, more drifting is required to approach the crusher complex to finalize support for the crusher chamber, installing crusher system and commissioning conveyor drift.  By the time the first drawbell is blasted, the ore factory concept would depend on the completion of the crusher complex as well as the conveyor system.    Mines normally respond to any issue encountered by proposing a temporary solution that mitigates the risk of delays. In New Afton for example, a temporary jaw crusher was installed upright in the conveyor drift in February 2012, after five months of blasting the first drawbell in 42  September 2011. At that time, the ore handling system was partially completed, where the conveyor belt was in progress along with completing the main gyratory crusher at the haulage level. It was not until January 2013 that the system was fully utilized for production purposes in which approximately over 50 drawbells were completed and nearly three quarters of the first phase, Block 1, was fully transferred to production crews.    2.3.2 Recognition of Flexibility in Construction   Impediments in construction processes and poor ground conditions which lead to excessive delays should be a strong incentive to prioritize the construction schedule and seek flexibility to improve construction performance. One dimension of flexibility is to utilize the conveyer system in the construction phase and improve mucking strategies and thus expedite the process. Having the conveyor system available in the construction phase can also add flexibility in the case where more drifting development is needed and extra equipment is brought to implement construction crashing.    Conveying and traditional truck hauling can be used concurrently or individually. In fact, the flexibility of switching between trucking and conveying in the case of breakdowns, maintenance or even utilizing both ore transporting systems in the case of fleet congestion along the decline access results in minimizing delays and improving performance in construction. The ore handling system must be fully completed and debugged in the beginning of the early construction phase within the ore body.  This flexibility saves time in mucking activities, reduces fleet congestion at shared access decline, and, as a result, increases the economic value of the project by minimizing the impact of delays on the construction schedule of the project.  43  A cost premium is required to make this option available, as the mine must spend money upfront and make this system ready at the time of initiating the undercut level. By prioritizing the construction schedule in which the conveyor system needed to be completed prior to the production phase, this system can be ready to be exercised when more crews and equipment are scheduled for developing multiple headings, as well as construction of multiple drawbells. If the value attained by speeding up this phase of construction and arriving at production faster outweighs the money spent upfront, the profit will improve the robustness of forecasts in project value and have a high potential of being accepted. At least, by keeping the production startup schedule on time would enhance the actual value that might be potentially decreased by delaying the production phase in which the interaction between development and construction may lead to unexpected delays.   2.3.3 Design Considerations for the Ore Handling System  The design of the ore handling system considers many factors, such as size of the ore body, depth of the footprint, geology, risks and hazards, and major structures, but, most importantly, the decision is driven by the cost and safety. In terms of shaft versus conveyor systems, the feasibility study conducted for the New Afton project (Hatch, 2007) concluded that due to the lower cost of building the conveyor haulage system, this option would be chosen over the option to build a shaft hoisting system. The study indicated that the design of having a dedicated conveyor ramp and independent access ramp would not have any advantage over the shaft hoisting system.  Thus, the mine decided to have a single conveyor ramp that could also serve as a primary access ramp.  The report mentioned that the design would cost 20% less than the 44  hoisting option, despite the fact that the unit operating cost per tonne of the shaft system is approximately 7% lower than the conveyor one.   Upon arrival to the footprint level, the ore body size influences the choice of having a haulage level. There are fewer drawbells in smaller mines (e.g., Palabora and Northparkes mines), thus small production fleet sizes is required as well as less distance is required to travel from one side to another.  The cost of building additional levels underneath the extraction level is less favorable for those smaller mines and, consequently, the crusher is often placed in the extraction level. In Northparkes, for example, a single permanent jaw crusher is located in the extraction level where trucks move more directly from drawpoint to crusher tip (Ross, 2008). This can save money in eliminating ore passes, haulage drifts, and associated ventilation. In contrast, New Afton mine decided to design a separate haulage level located underneath the production level to minimize the interaction between the construction and production crews. Intuitively, however, large caves – 1000s of drawbells – more often build separate haulage levels to minimize fleet congestion in extraction levels due to the large number of active drawpoints.    2.3.4 Current Design and Construction Challenges While different designs of ore handling systems can serve one purpose of sustainable production capacity, in terms of construction flexibility, it is challenging to use the current design of the mine to utilize the ore handling system in the construction phase.  The mine faces challenges in construction to bring the system ready and available at the final stage of construction phase because the current design is optimized objectively for production purposes. As shown in Figure 2.1, the crusher complex is designed to be somehow in the middle of the footprint and underneath the production. This fits perfectly for all production fleet above in the extraction in 45  which no LHD would travel more than half the distance of the ore body length. Also, pillars between haulage drifts are large enough to permanently support those drifts and prevent them from excessive stresses.    However, in terms of construction scheduling, it is impossible to build the crusher system before starting the development in the footprint.  Moreover, time is needed to complete the ore passes and haulage drifts needed to be used in construction. Both are physical constraints to completion of the predecessor, approximately less than 700 m of drifting to connect the footwall drive or mine access to the system.  Considering the time to complete this system, many drawbells and development meters would have already been completed using the truck hauling system.   2.3.5 Design Considerations for Flexibility  Three different designs are proposed below to be able to serve both construction and production needs.  Although the design is built on a particular case study, the same concept can be used as a framework of design for flexibility in terms of need-for-speed in construction. Those design alternatives are based on the assumption that undercut sequencing commences from west to east direction using advance undercut strategy.    In the case of different undercut sequencings, as it will be discussed later in this chapter, the same major concept of design philosophy can be applied as follows: 1. The first objective is to locate the major haulage system components near by the undercut starting point.  Thus, as soon as the development in apex, undercut, and extraction starts, the construction of the crusher would have been completed and commissioned ; and  46  2. The second objective is to have the minimum development meters of haulage drives in order for the ore passes and ventilation to be built right away.   Design for flexibility requires possible changes in the existing New Afton design and construction plan.  One challenge is finding one optimum design solution and it is not always the case. All the following proposed design options are feasible, but each one has its cost and time implications.    Design option 1: Utilize a jaw crusher in the extraction level temporarily.  The first design alternative is to have a jaw crusher in the extraction level intended to be temporarily utilized in development and construction within the foot print, as shown in Figure 2.2. This is a fast, temporary solution in those mines that have to design a permanent haulage level and the location of the crusher haulage system is constrained by the geology or production factors.  There is no need to change the design of the existing haulage level and, thus, the permanent crusher can be used later in the production process. The permanent gyratory crusher in this case can be built on schedule. This way of speeding up the mucking process requires the conveyor belt to be ready to transport the ore from the crusher to surface.  Prince et al. (2013) discussed reasons that contributed to the delays of building the crusher complex and conveyor transfer chamber. The postponement of building the crusher and conveyor transfer chamber (CTC) occurred due to redesign of the size and location of the crusher chamber and relocation of CTC. Thus, at that time, the mine put plans to place a jaw crusher father up in the conveyor system.  47  Yet to proactively manage uncertainty, this design option should be realized early in the planning phase as the size, location, and procurement of the crusher needs to be planned accordingly. The conveyor schedule needs to be prioritized in such a way that the conveyor and temporary crushers are used. Cost premium is simply the cost of having the extra crusher in the extraction level during the construction as well as the portion of upfront cost to build the conveyor earlier than normal, as the value by improving the speed of mucking and overall development can outweigh the additional cost. One disadvantage lies in the fact that having this in the extraction level results in other sources of delays due to congestion during full-scale development and production phases.   Design option 2: Move the gyratory crusher nearby to the construction area.  To eliminate any ore handling component in the extraction level, another alternative is to move the crusher complex nearby the starting point of the undercut and extraction, as shown in Figure 2.2.  In the case where it is sequencing from the west, as in New Afton, this option results in less development from access drive to crusher complex. The system will be ready as soon as the crusher station, chamber, convoy chamber, and conveyor belt are completed and commissioned. Particular to New Afton, moving the crusher complex from the middle where the influence of the FW fault exists two locations away from the fault zones adds extra benefit to the mine team.   The cost premium to build the entire ore handling system earlier has to be allocated in the first two phases of construction before starting development within the cave footprint.  Also, it requires additional haulage drifts, especially for those concerns to farther away drawpoints and associated ore passes. Despite the increase in capital expenditure and, thus, present value of construction phase, the overall value of the mine will be increased by shifting the production 48  earlier. One disadvantage is that treating those far away drawbells on the east will require LHDs to travel the entire route from west to east in the production phase. To minimize this distance, the last group of ore passes can be shifted toward the middle of the ore body footprint.   Design option 3: Build two gyratory crushers in the haulage level.  One way to solve this problem of having uneven distances of hauling ore is to build two smaller crushers in the haulage level connected by a one-leg conveyor belt, as shown in Figure 2.2. The first crusher is scheduled to be ready before construction begins in the extraction and located near the starting zone. The second can be completed later during full-scale production to sustain the mine production target. Similar benefit as those in option 2 to construction are expected from this option, as well.  In terms of production, in case of crusher breakdowns or maintenance, one can be used over another and maintain production even with lower capacity. Having regular size crushers can give system management the capability to use one or both crushers if they want to increase the facility production or change the design during the execution.  Cost-benefit analysis could be conducted to this option compared to design options 1 and 2. 49   Figure 2.2 Three design options for the ore handling system (plan view) 50  2.4 Flexibility in the Extraction Level In cave mining systems, an extraction level is the main production level in which caved material from an undercut level flows down through drawbells to drawpoints where it is extracted and transported to the surface by means of an ore handling system.  As opposed to the apex and undercut levels, the extraction level is a permanent structure during the entire life of the mine production phase and requires extensive amounts of quality construction work and ground support, since it is crucial to sustain the durability and stability of the main production level.   The most common extraction level layouts are the El Teniente and Offset Herringbone layouts, as shown in Figure 2.3.     Figure 2.3 El Teniente and Offset Herringbone layout designs (plan view)  Many mines are currently using the Offset Herringbone layout, such as Palabora (South Africa), Northparkes (Australia) and Diavik (Canada). Others planning for this layout include Resolution Copper (USA) and DOZ (Indonesia). In contrast, Oyu Tolgoi (Mongolia), Grasberg (Indonesia) 51  and New Afton (Canada) are examples of those mines which have decided to implement the El Teniente layout. Several future potential underground caving projects are currently in the feasibility stage and considering selecting an appropriate layout (e.g., Kwanika, Kemess, and KSM projects in British Columbia, Canada).  Construction of an extraction level is critical to the overall mine construction schedule since the production capacity of a panel cave, for example, relies on continuity in the sequence of opening new drawpoints; while  a block cave, on the other hand, depends on the initial completion of development infrastructure for the entire ore body block. Construction of an extraction level tends to be on the critical path in the development of all horizontal infrastructure levels, so any intention to speed up the mine construction process focuses significant attention on ways to accelerate this level.    In terms of flexibility among different extraction level layouts, the El Teniente option can provide more stability to pillars and a faster construction process. In terms of development, one significant advantage of the El Teniente layout is that it requires less ground support in turnouts, and provides a faster development process along drifts; however, additional support in intersections (e.g., bull noses and camel backs) and additional drifting are required, see Figure 2.3.  The El Teniente layout (named after Codelco’s El Teniente mine in Chile) derives from the logic that developing straight linear drifts would most likely be faster than those with drawbell turnouts.  52  2.4.1 Major Decision Factors in Extraction Level Layout Design  The preference for the El Teniente extraction level may be overridden by three significant factors relating to safety, operational and geotechnical aspects. In mines where the risk of a mud rush is high, Offset Herringbone provides a safer environment than the El Teniente option. In the event of a mud rush, equipment and production manpower would tend not to be pushed severely into the opposite drawpoint, tending to be pushed more moderately into the side of the extraction drift instead. In anticipation of a high mud rush potential, for example, the DOZ mine in Indonesia decided to implement the Offset Herringbone layout for safety reasons (Botha et al., 2008 & Setyadi et al., 2013). In the case of the Northparkes mine an electric LHD fleet operates from one side of the extraction level layout, serving one crusher placed in the extraction level (Ross, 2008). The alternative diesel LHD layout would imply construction of two independent crusher systems on opposite sides of the footprint. In planning the future Resolution copper mine, the Offset Herringbone layout was preferred over the El Teniente layout because it was considered to be adapted best to electric LHDs (Pascoe et al., 2008).    In terms of geotechnical constraints, depending on the direction of principal horizontal stresses and major structural discontinuities, the optimum design is chosen which minimizes ground stability issues. It may be advisable to examine the larger drift intersection area associated with the El Teniente style. Another concern may be over the design of the direction of the extraction drives (strike drives) and drawpoint and drawbell drives (crosscuts). The level of ground support needed may need to account for the nature of the in situ horizontal stresses and major geological structure. The key factor is to choose the orientation of the extraction layout so as to be perpendicular to any major geological structures as well as the major principal stresses. 53  Otherwise, stresses can build up on the intersections of drawpoints and impact adversely on pillar stability. Table 1 discusses the advantages and disadvantages of both extraction layout styles.  Table 2.1 General comparison between Offset Herringbone and EL Teniente layouts Offset Herringbone layout Advantages  El Teniente layout Advantages   Increased intersection stability from being offset and staggered   Increased operation efficiency since more room available to maneuver   Allow for LHD electrical cables   Less drifting due to staggered drawbells  Improved mud rush safety for operators not being pushed to opposite drawpoint  Allows for ideal draw condition (zone of influence overlapped) and good interaction between drawpoints    Easiest and fastest development (straight full cycle drifting)   More stable and stronger pillars (shorter minor apex with respect to major apex, pillars: regularity and bigger pillars)  Ease of traffic control (LHD can back into opposite drawpoint and turn around)  Allow for ideal draw condition (zone of influence overlapped) and good interaction between drawpoints Offset Herringbone layout Disadvantage El Teniente layout Disadvantages    Difficult to develop as many turns exit  Difficult to permanently maintain  bullnose structures (loss of pillar)  Not allowing LHDs to back into adjacent drifts    Not suitable for LHDs electrical cables   Ore can flow into drifts and interfere with other drawbells because of the straight line crosscuts  only allow LHD access to drawpoints from one side of given drift   Mud rush hazard (operator being pushed into opposite DBs)  2.4.2 Extraction Level Design Considerations    The extraction level design is influenced by the degree of fragmentation realized within the overlying caving zone.  The fragmentation size distribution determines the size of draw zones above drawpoints and, therefore, the required design spacing of the drawbells. Moreover, both geotechnical factors and the undercut strategy (e.g., pre, post, or advance undercut strategy) can influence the design. The anticipated levels of stress that build on the extraction level and the 54  nature of major structural discontinuities present will tend to determine the support planning for the extraction drifts. The spacing and support for drawpoints and drifts will serve the objective of maximizing the ore recovery by enabling the selection of larger machines (e.g. LHDs) in the minimum-acceptable size of drift. An example of the design of the El Teniente layout is presented in Arancibia et al. (2008).  Extraction level design addresses the layout between a series of extraction drives (strike drives), drawpoint and drawbell drives (crosscuts), and boundary drifts (rims) that is optimal for the production cells (drawbells).  This includes the design of the spacing of the major apex, the distance between draw zones along extraction drifts, and the minor apex, and the distance between draw zones along drawpoint drifts, as shown in Figure 2.4.   55   Figure 2.4 Extraction level design parameters – A: distance between draw zone in drawbell, B: distance of draw zones across minor Apex, C: distance of draw zones across major Apex, D: width of extraction drive, and E: distance between two extraction drives (pillar)   2.4.3 Drawpoint Spacing Considerations     Another design issue is the tendency among cave mining operations to adopt aggressive designs by increasing the size of the rock pillar to reduce upfront capital cost and to maximize production using larger LHD machines (van As & van Hout, 2008).  Increased spacing reduces capital costs because fewer drawbells are constructed and increased pillar stability occurs.  Construction of fewer drawbells means a faster ramp up to production, higher production rates and reduced 56  drawpoint ground support (e.g., less steel sets, etc, used to support drawpoints where pillars are larger).   However, increased spacing can mean no overlap between draw zones (independent draw) and thus the ore recovery may be jeopardized by admitting early dilution entry and increasing the potential of reduced ore recovery.  Once construction of drawpoints commences, then it is very difficult to change the spacing and layout of the extraction level.  In contrast, close drawpoint spacing (interactive draw) results in smaller pillars that give rise to good ore recovery. However, this can lead to excessive stress above those pillars that potentially could be damaged and lead to support issues, increased rehabilitation costs and delays in production.   Excessive drawpoint spacing results in reduced capital cost (fewer drawbells need to be constructed), and also can technically and economically favor the design of larger drifts that suit larger production machines. However, Laubscher (1994) argued that decisions on designing or selecting production equipment sizes should be based on the correct assessment of the required draw zone and associated drawpoint spacing with respect to fragmentation and draw. This is to ensure high ore recovery and proper ore reserve reconciliation.   Thorough design requires adequate knowledge about the rock mass and stresses expected around the extraction level. Then, based on caveability and fragmentation assessments, the proper design of production level spacing and dimensions can be optimized.  The implications of increasing the drawpoint spacing are discussed in Van As and Van Hout (2008). This complex design challenge of conflicting factors can benefit significantly from the development of improved production 57  modeling tools. A trade-off analysis needs to be made in such conflicting circumstances to achieve the optimum design.  Another concern is the direction of the extraction drives (strike drives) and drawpoint drives (crosscuts). It is suggested that to lessen the amount of ground support needed, the in situ horizontal stresses and major geological structure should be considered.  The key factor is to choose the direction that is as close to perpendicular to major geological structures and to major principal stresses. Otherwise, stress will build up on the intersections of drawpoints and impact their stability.    In the case of New Afton, the direction extraction drives have changed from north-south to east-west to minimize the intersections with faults.  Straight-through design in the El Teniente layout allows crosscuts to be parallel to the principal stresses, as shown in Figures 2.5 and 2.6.  Another design issue, in case of any potential pillar failure in one of the main drives, the mine decided on the direction of the strike drives to be in the shorter direction of the ore body to minimize the impact of any potential risk of failure of ore recovery.58   Figure 2.5 Plan view of New Afton El Teniente extraction layout (Source: New Afton mine, 2012) N 59   Figure 2.6 Plan view of New Afton mine extraction levels – the 100th completed on 27th may 2014 (Source: New Gold, 2014)60  2.4.4 Extraction Crosscut Development   Eliminating avoidable turnouts and reducing small scale mining cycles may be key to increasing construction rates. This is to the contrary in Offset Herringbone, in which its many heading turns and brows require shorter cycles and additional ground support. In contrast, the development of the El Teniente crosscuts that link the extraction drifts with drawbells are more simply developed as straight drifts. Those crosscuts, however, are longer, which requires more total drifting in the El Teniente design. Thus, as illustrated in Figure 2.7, in order to model one crosscut, six 4-meter cycles are simulated in which the El Teniente layout allows development of mining cycles to start from one side, then advancing through the entire crosscut.  This contrasts with the Offset Herringbone, in which the first drawpoint drift and associated drawbell drift must be completed first within the drawbell zone (e.g., cycles 1 to 6) before the second drawpoint can begin (e.g., cycles 7 and 8). In this case, four 4-meter drifting cycles and four 2.5-m cycles are assumed to complete one crosscut.     Figure 2.7 Comparison between Offset Herringbone and El Teniente layouts – in terms of drifting cycles, turnouts and intersections (plan view) 61  Another benefit is that El Teniente provides additional temporary access to development and construction zones in which interference with dedicated production access can be omitted in the early stage of production. This grants easy and exclusive access to construction zones in which logistics of construction material and equipment is separated from production logistics. It will minimize risk of delays especially in panel caving where production, construction, and development crews work together in three adjacent zones.  The utilization of a drawpoint drifts as a temporary access (fringe drive) is evidently an advantage in El Teniente as a straight through layout. Eventually the fringe access will become a typical drawpoint drift used in production. As shown in Figure 2.5, while five entries from Footwall drive to extraction level are available, two of them can be used as fringe drives, one temporary access that is currently used in development and construction of Block 1.  2.4.5 Recognition of Flexibility in Construction   In contrast to the early stages of development, in which a limited number of headings are available, at full-scale construction, more open faces are ready for development, but the speed is dictated by the advance rate of both the extraction and undercut level based on the undercut sequencing strategy exercised.  For example, New Afton implemented the advance undercut strategy where extraction level development and construction lag behind the undercut level development.  This allows for a low-stress environment for extraction level development and construction.  More discussion is given in section 2.5.    62  Several factors affecting construction crashing of multiple face heading depend on: 1. Undercut strategy (depends on the speed of development in advance undercutting); 2. Availability of opening faces (depends on the stage of development); 3. Capacity of ventilation (depends on design criteria); 4. Utilization of large equipment (depends on the spacing and orientations of drifts); 5. Availability of trained equipment operators (can take up to six months of training); and 6. Procurement of equipment purchase (can take up to two year from inventory).  In multiple drifting, crashing is possible by improving resource utilization.  This is subject to availability of ventilation, ore handling system, logistics, and resources. However, the fact that the decision to select between Offset Herringbone and El Teniente layouts will not often have the need to change equipment selection, ventilation capacity, crew size, infrastructure requirements, undercut sequencing, and extraction drives. The availability of the ore handling system during this stage can add significant benefit in terms of increasing the amount of ore transported to the surface and avoiding risk of delaying mucking activities.   The El Teniente layout provides the means to exercise crashing by: 1. Utilizing full drifting mining cycles in drawpoint and extraction drives by developing straight line drifts starting from one direction and avoiding unnecessary turns along drawpoint drifts;  2. Utilizing fringe drives by using drawpoint crosscuts as temporary access drifts to allow for flexible movements of material and labor to development and construction zones and proactively control delays in the case where additional equipment is needed; and  63  3. Implementing crashing by utilizing more resources – additional equipment crews – as the additional new faces opened up results in less constraints to resource utilization.    In choosing the El Teniente design, a mine should be able to implement full scale cycles along drawpoint and drawbell drifts, if needed, by improving the utilization of resources in which drawpoint drifts can also be used as temporary access drifts to enhance the logistics of construction equipment, material, labor, where full development mining cycles can be implemented.  The available technical literature shows very little attention has been given to directly comparing the performance of both these layout options with respect to development rates and meters advanced.  2.5 Flexibility in the Undercut Level The undercut level is a temporary level located above the extraction level in which a horizontal slice of adequate dimensions is extracted to initiate caving of ore above it. In order to ensure caving occurs, a caving radius or hydraulic radius (an undercut area over its perimeter) must be removed just above the drawbells and at the base of the mining block. As broken rock is removed from a drawpoint, ore above it will start to collapse due to the primary fragmentation in the caving zone. Vertical and horizontal propagation depends on progressive removal of ore and the progress of opening new drawpoints.  Laubscher (2000) indicates that caveability is a function of the size and shape of an undercut as measured by the hydraulic radius and the rock mass strength, as characterized by Mining Rock Mass Rating (MRMR). Figure 2.8 shows a cross section of the horizontal infrastructure. Figures 2.8 and 2.9 show the undercut level design in New Afton.  64  The apex level is an additional level located above the undercut and is considered to be part of the undercut system as shown in Figures 2.8 and 2.10.  It can significantly add advantages in building cave mining systems because it is used to ensure that 100 % of undercut blasting is completed effectively to maintain the stress shadow in the extraction level. Most small block cave mines do not consider apex level and all undercutting activities are done in undercut drives because of the cost associated with it. The case study considered herein utilizes apex drives designed to ensure that undercut blasting is completed effectively.  After blasting two undercut strips, each strip is approximately 8.5m by 25m, apex drives can allow for visual inspection into the undercut level. If any voids or oversize rock are evident, they can be blasted to prevent risk of ore stacking and to ensure maintaining the flow of material to the extraction level. The height of the apex level is approximately 17 m above the undercut and 34 m above the extraction level.    Figure 2.8 Cross section (North-South) of New Afton horizontal levels – apex, undercut and extraction levels are 17 m apart (Source: New Afton mine, 2012)65   Figure 2.9 Plan view of New Afton Undercut level – undercut advances from west to east (Source: New Afton mine 2012) N 66   Figure 2.10 Plan view of New Afton Apex level– 17 m above the undercut level (Source: New Afton mine, 2012)N 67  2.5.1 Undercut Level Design Considerations The typical design of the undercut level involve consideration mainly of rock mass strength, major structural geology, and principal horizontal stress orientation to promote cave initiation and propagation and to sustain production capacity (AMEC, 2010). The quality of undercut development determines the long-term performance of the operation in the production level. Several factors considered in the design are placed herein into three major classes of factors related to: (i) the process of undercut development (process), (ii) the actual size of the drawbell with respect to pillars (dimension) and (iii) the method of undercutting (strategy).   These factors are outlined below as: 1. Undercut starting point – Process 2. Direction of undercutting – Process 3. Length of undercut face – Dimension 4. Direction of undercut face – Dimension 5. Height of undercut – Dimension  6. Spacing of undercut – Dimension 7. Undercut technique – Strategy 8. Undercut sequencing – Strategy 9. Rate of undercutting – Process  As a temporary structure located above the extraction level is essential to induce the cave, the first decision with respect to undercut dimension is to determine the height and spacing of the undercut, see Figure 2.8.  It should be reflected on the undercut strategy used depending on the 68  characteristics of the surrounding rock mass. Then, where the undercut should start in and how it should advance to should come next. The height and spacing of the undercut depicts the size of the pillar protecting the production cells below (drawpoints).  The extraction level major and minor apex spacing determined by the assessment of the draw zone dictates spacing of a typical undercut strip, a thin slice of rock drilled and blasted above each drawbell in one undercut cycle. In New Afton, the height of undercut is 17 m and the design consider two strips – approximately each strip is 8.5m by 25m – above each drawbell drilled and blasted from undercut drives and then assessed from a unique above level called apex level.    In the design phase, consideration is given to the process of undercutting, as it is important to select the starting point of the undercut and direction based on the orientation of principal stresses and major structural discontinuities to purge the impact of abutment stresses on the extraction level (AMEC, 2010). The starting point is often chosen to be where the high-grade ore is located regardless, in some cases, if the high grade is in the side or the middle of the ore block. Smaller-sized mines (e.g. New Afton and Northparkes) prefer to initiate their undercut where a weaker rock mass is located – very low MRMR – to ensure caveability occurs with minimum required hydraulic radius. Particular to New Afton, this decision is mostly based on how fast the mine can start production and emphasis was put on where the highest grade is located. Undercutting starts on the west side and advances to the east where the old open pit is located. Commencing closer to the main infrastructure and away from the existing old open pit is a critical decision made by the mine management to achieve the production goal.   69  In terms of undercut direction, the undercut drives should not be parallel to major structures and principal stress to protect the brow of the underneath drawpoint drifts and lessen the rock support needed (AMEC, 2010), see Figure 2.11. Undercut drives must be as perpendicular as possible to a major structure. With respect to undercut face, it also should not be parallel to a major structure, otherwise stress will build up on extraction drives and sometimes can elevate more dramatically than virgin stress. Likewise, the undercut face direction should not be parallel to major principal horizontal stress.    Figure 2.11 Schematic diagram showing suitable undercut drives and undercut face direction with respect to major structural discontinuities and major horizontal stress (plan view) 70  In terms of undercut strategy, three major undercut techniques are commonly adopted in practice. Each one has a different influence with respect to the induced stresses on the extraction level and, consequently, impacts the amount of ground support, rehabilitation, and reinforcement needed in the extraction level. In pre-undercutting, undercut development takes place before the development of the extraction has been completed. In contrast, post-undercutting refers to the technique in which the undercut is developed and completed after the development of the extraction level commences as in the case of Henderson mine. This technique is recommended only in mines where a stronger rock mass is expected.   In recent years, however, several mines adopted the advance undercut strategy in which the development of extraction drifts and the construction of drawbells lagged the development of undercut by certain distance called “Veranda zone” (Abutment zone), as shown in Figures 2.12 and 2.13. From a geotechnical point of view, this strategy allows for the extraction level to be developed in a de-stressed environment behind the undercut abutment zone in which stress redistribution takes place around this zone and away from the extraction construction zone. The vertical stress may cause problems in the permanent extraction level and could result in additional rehabilitation costs. Despite the complexity of such methods in which the process of construction is coupled between these levels, most current mines adopt this technique due the expected low MRMR.  71   Figure 2.12 Process diagram of the sequencing of the “Advance Undercut Strategy” (Elevation) 72   Figure 2.13 Advance undercut strategy - production, constriction, and development zones (Elevation)  The undercut advance rate needs to be constant to ensure the horizontal and vertical propagation of the cave. In the pre- and post- undercut strategy, the goal is to advance as fast as possible to promote caving. However, in the advanced undercut strategy the undercut development rate should not exceed the progress of drawbell construction underneath in the extraction level, so as to maintain the shadow stress zone for the active construction area. In that scenario, the undercut face length should be kept as small as possible. As shown in Figure 2.10, the face length is approximate 130 m that equal to the shorter dimension of the ore body and the undercut advances at the same rate as the rate of extraction.   2.5.2 Advance Undercut Strategy from Design to Construction  The advance undercut strategy has more advantages in the construction process because more openings in the apex, undercut, and extraction levels are available during every Advance Undercut Progress Cycle (AUPC). However, this process is a complex series of partial 73  development of undercutting coupled to the construction of the extraction level below. Multitasking of equipment utilization may take place in those levels simultaneously in contrast to the pre- or post- undercutting, in which either the extraction or the undercut level is available at any given point in time for development.  However, the complex sequencing arises due to the fact that the undercut advance rate is constrained by the speed of building the extraction level underneath the stress shadow zone or abutment zone shown in Figure 2.11. This sequencing with respect to extraction level ensures minimal damages occurs to extraction level excavations.   In terms of the construction process, the advance undercut strategy can be slower than the post-undercut.  Post-undercutting can provide a faster time of production, but would most likely be implemented in good rock mass conditions, as opposed to pre-undercutting which  is very slow in achieving production targets. The complex sequencing between extraction and undercut levels requires much attention to resource allocation and is undeniably worth examination. It should be stressed that the greater the lag time between the two activities in the two levels, then the greater the load from the muck pile of the cave that is induced on the extraction level will be. This may cause rehabilitation and more rock reinforcement.   As shown in Figure 2.13, the five distinct working zones limit the ability to exercise development and construction anywhere without restrictions within the ore body at any current state of undercutting. Apex, undercut, and extraction drives are developed in the abutment region (Zone 5). Also, new undercut strips developed to create the stress shadow zone above extraction is drilled and blasted in the abutment region (zone 4).  Zones 2 and 3 are dedicated regions for 74  constructing new drawbells and developing new crosscuts in the stress shadow region respectively.   Development of undercut is vital to the production schedule since the availability of new drawpoints in the production phase depends on the progress of the undercut above it. However, using the advance undercutting strategy puts more pressure on the speed of undercutting, since the construction of drawbells requires more time and effort than undercut activities and, thus, more effort should be put in the extraction level.   2.5.3 Recognition of Flexibility in Construction  With the technical restriction of the unavoidable coupling of the development of undercut and extraction levels together and having a specified working zone for each work package one question important arises:  Are we able to increase the number of available open faces in every working zone for every AUPC? One way to make this happen is by altering the undercut sequencing strategy from the current one-direction sequencing from the side -- “side sequencing” -- to two-direction sequencing from the middle -- “middle sequencing.”   However, another questions then arises:  How much gain in construction productivity and speed can be achieved?   The flexibility that lies in middle sequencing allows for providing almost twice the number of available open faces and accesses to crosscuts within the stress shadow zone that may potentially permit management to increase the amount of equipment utilized, especially in the early stage of development. The objective from the flexibility is to accelerate the early stage of construction by completing the minimum required number of drawbells that sustain full production targets as fast 75  as possible. In other words, the shorter the early stages of development and construction are, the faster the rate to full production is, and the more economic value would be attained.   New Afton management decided to initiate undercut sequencing from the west side (side sequencing) and advance to the east. Due to the shape factor of the ore body and other undercut design characteristics, there are only 4 – 5 available crosscuts for drawbell construction and 18 – 22 available drifts for one undercut face.  For middle sequencing, however, the two undercut faces that may progress in the opposite directions can allow for 8 – 10 and 36 – 44 crosscuts and available drifts, respectively. In fact, this would allow for increasing the optimized number of equipment assuming that ventilation has been designed for such a move.   Approximately 47 active drawbells (94 drawpoints) are required to yield maximum production targets in New Afton.  The production ramp-up phase depends heavily on the opening of new drawpoints, since recommended production draw rate from each drawpoint should not be surpassed (Laubscher, 2000). Exceeding that rate results in a huge gap between the cave back and cave ground  in the caving zone and may lead to the potential of air blast, similar to what happened to Northparkes E26 block (Ross & Van As, 2005).  This production draw rate also considers other factors, such as fragmentation, in which more time is required for broken rock to flow through the cave muck pile, resulting in better production fragmentation.    Many factors contribute to the decision to sequence from the west to east. The most significant one is related to the economic value where the high-grade ore is located in both sides of the ore body (Block 1 and 3) and divided by low-grade pillar in Block 2. The decision to aggressively 76  acquire the easier block (Block 1) on the left side outweigh the decision to develop a few hundred meters in the Footwall drive and then mine the second, farther away, Block 3. In fact, it is a decision to attain the ore faster and not to spend a few months and start from the other side. Also, closer high-grade blocks are near to underground infrastructure and away from the pit slope, giving time to discharge water from the old pit that potentially ingress the mine and affect the production.   In contrast, middle sequencing can promote higher speed and longer-term benefits than side sequencing. It can be implemented just in the middle of the ore footprint and also in the middle of a block (e.g., Block 1 in New Afton). Both options have their benefits and drawbacks, as shown in Table 2.2. The undercut sequencing flexibility based on each of the two cases presented in Figure 2.14 will be discussed in more detail. 77     Figure 2.14 Side-sequencing and Middle-sequencing cases 1 and 2 (plan view) 78  Option Case 1: Middle sequencing commencing from the middle of Block 1. Implementing this flexibility in the initial Block 1 to exercise crashing in the early stage of development can decrease the production start-up phase.  Among the three blocks, Block 1 is located in the west and comprises 65 drawbells relatively considered to be medium to high grade. Full production capacity requires approximately 45 drawbells (90 drawpoints) to sustain 11,000 tpd. Since the mine management planned to build an average of four drawbells per month (DB/month), the start-up phase may take up to one year in an ideal situation, where no risk or uncertainty is revealed. Any means to reduce this phase will improve the economic value at stake, in which the mine experiences slightly higher than 3.6 DB/month. The cost premium is to utilize an additional amount of equipment that is optimized based on the interaction between the construction of undercut and extraction level sequencing strategy.    Option Case 2: Middle sequencing commencing from the middle of the footprint between Block 2 and Block 3.  In terms of the case in which sequencing starts from the middle of the cave footprint, exercising this option requires time for developing the Footwall access drive from the east side to the middle of the footprint.  In New Afton, this may take up to approximately 375 meters of single drifting in the Footwall. Based on an average planned figure of meters heading per day, that translates to a minimum of two months of delay to start developing the footprint.   In fact, this option may also decrease the quality of the ore grade distribution, in particular, to New Afton because production undercutting will commence in both Block 2 and Block 3, where Block 2 is low-grade ore. In that case, it is expected to have low-grade ore in the shortened start-up phase until opening the first 47 drawbells. The economic value obtained by shifting the production phase should also be examined against the decrease in ore grade.   79  Another factor to consider is the option to increase the full production phase in which any increase in the metal price above a certain threshold will trigger the mine management to increase the full production capacity to increase revenue.  The production option is beyond the scope of this study. The intent herein is to show how much time can be saved in construction and development. Advantages and disadvantages of these options illustrated in Figure 2.14 are discussed in Table 2.2.   Table 2.2 Comparison between side and middle sequencing specific to New Afton mine Option  Advantages Disadvantages Current practice    Commence from the West side and advance toward the East   Cave initiation away from the open pit  Fastest access to high grade ore and quick to production   Slow of early development and construction  Long production start-up phase   Flexibility U/C Option Case 1   Commence from the Middle of Block 1 and advance toward the East and West  Ability to crash schedule and work in double open faces during construction of Block 1 only   Faster initiation of the cave   Production from high grade ore    Delay few weeks to start production phase  Additional money to spend upfront on equipment and ventilation  Flexibility U/C  Option Case 2   Commence from the Middle of the footprint and advance toward the East and West  Ability to crash schedule during all construction phase and work in double open faces  Faster initiation of the cave front   Delay few month to start production phase   Production from high and low grade ore   Additional money to spend upfront on equipment and ventilation  Additional money to spent upfront to increase the capacity of the ore handling system to make the production available  80  2.6 Conclusions Recognition of flexibility offers important insights into the design and planning of cave mining systems. In this chapter, three flexibility options in three important infrastructure levels in cave systems are identified.  Those are summarized as follows: 1. The first flexibility option concerns the haulage and ore handling system utilizing the conveyor system with or without the truck hauling system in the early and full construction phase.  2. The second flexibility option involves employing the El Teniente layout for better construction performance.  3. The third flexibility option is to change from single-side sequencing to double-side sequencing from the middle to be able to improve resource extraction capacity.   The next chapter is concerned with the second step of planning for flexibility which includes modeling these three identified strategies identified. Simulating the process of construction and development using the discrete event simulation technique is undertaken to investigate how much benefit can be achieved. The New Afton mine current construction practice is emulated, validated, and benchmarked, and then compared to each different strategy.  Results were obtained for construction completion dates where operating uncertainties were incorporated in all models, since they played a significant role in construction performance. Ore grade and metal value uncertainty were not considered in these models.    81  Chapter 3: Modeling of Flexibility in Cave Mining Construction  3.1 Introduction This chapter discusses simulation models that can be used to examine the improvement in construction performance when specific type of flexibility is recognized. The main contribution of this chapter is to develop and describe a method capable of modeling the development and construction processes with respect to the advance undercut strategy, which integrates the geotechnical and technical uncertainties, using the framework of discrete event simulation (DES). Several scenarios are developed to investigate the impact of risks on construction schedules.  The benchmark scenario models are created based on actual data from an existing case study and thus simulate the entire development and construction process of New Afton mine. These scenario models are compared to the benchmark models. All scenarios have been simulated throughout two distinct models:  development and construction models.  Simulation results are used to investigate and examine the enhancement of construction productivity compared to a conventional construction strategy as well as provide insights into the design and planning for flexibility.  It is critically important to emphasize that the mine management can alternate between the two ore handling systems or switch back to the truck-haul system in the case of conveyor or crusher breakdowns, since the mine has another access decline.  Moreover, the mine can switch to side-sequencing from middle-sequencing and advance only in the high grade ore if metal prices drop to specific threshold levels. Yet, the option to achieve a higher performance rate by progressing from both sides is available if the prices increase. However, it is often difficult to switch between 82  the El Teniente and Offset Herringbone layouts because many considered design factors constrain moving from one to another during construction. If there any geotechnical, safety, or production advantages to changing the design during construction to Offset Herringbone, the mine management can strategically plan to change the layout style in the subsequent blocks. It is difficult to alternate between El Teniente and Offset Herringbone layouts while implementing middle-sequencing strategy.  This chapter describes how models are created in ExtendSim© software (Imagin that Inc, 2010). The section on model evolution discusses how the development and construction models have evolved from simple to complex models. Subsequent sections give details regarding the model assumptions and setup and how these models are built in the discrete event simulation (DES) tool. To ensure reliability of the results obtained from simulation models within the intended purpose of the study, the benchmark models have been verified and validated and, then the scenarios are tested against the benchmark model.   3.2 Literature Review The purpose of this literature review is to discuss the published studies on the application of DES for modeling underground mining systems.  Most of the DES studies cover performance of haulage systems, optimization of equipment selection, and evaluation of underground development. Because there are extensive amounts of literature and reviews on the application of simulation and optimization in surface and underground mining operations, only a few specific publications on the application of DES in underground mining and block cave operations have been discussed.  83  In the last decade, simulation has become a very popular technique for designing models of production systems that mimic the actual operation and examine different scenarios within a sensible cost and timely manner without the need to carry out real-life experiments.  Its purpose is to aid mine planners in studying various design alternatives and configurations, specifications, and allow them to make critical decisions and understand the system. However, simulation cannot be used exclusively to solve complex optimization problems (Greberg & Sundqvist, 2011).  In this case, simulation and optimization techniques must be integrated to solve these problems. Several researchers have discussed the advantages and disadvantages of using dynamic simulation (e.g., Labrecque, et al, 2012; Li, 2012; Banks et al., 2010; Hall, 2000).    Newman et al. (2010) provided a comprehensive review of optimization and simulation models and techniques used to improve strategies and tactics in mining operations.  Extensive operation research (OR) models intended for surface mining have been developed for ultimate pit design, open pit block sequencing, and equipment selection and maintenance.  In particular, simulation has been widely applied for production scheduling and equipment utilization. This is somewhat due to the common characteristics of existing open pits in contrast to underground mining which in OR models have been developed based on the envisioned mining method used for the specific size and shape of the ore bodies. Li (2012) provided a current review of DES models related to open pit and underground operations. DES models stochastic dynamic systems in which the state variables change only at discrete sequences of events (Greberg & Sundqvist 2011; Banks et al., 2010). Simulation of underground mining methods is lagging the one for open pit mining.   84  3.2.1  Application of DES in Underground Mining Dynamic simulation in underground mining has tended to focuses primarily on the analysis of one component of the handling of ore, and has been commonly applied to the study of production rates and equipment utilization in production scheduling. Topuz et al. (1982) used DES to simulate the movement of coal from the mine face to the secondary or the mainline transportation network in room-and-pillar mining.  These researchers compared production rates of two haulage systems:  shuttle car/belt and shuttle car haulage. By conducting several runs of different haulage units, feeder capacities, and discharge rates, Topuz et al. (1982) identified the optimum number of haulage units to maintain production, above which an additional haulage unit did not provide a significant increase in production rates.    Hall (2000) used DES to identify truck fleet requirements for achieving production targets of a long-hole stoping project.  Hall (2000) modeled truck haulage systems, including a typical decline located at the bottom of an existing open pit. Several cases were run with different levels of truck fleets for development, filling, and production. Hall (2000) found that 12 trucks was the optimum number necessary to achieve maximize truck fleet utilization.  The maximum number of trucks was chosen by avoiding queuing at one loader and another was ideal.   In terms of conveyor belt haulage systems, McNearny and Nie (2000) developed detailed models for simulating a haulage system for a longwall and continuous mining underground coal mining. After McNearny and Nie (2000) built an initial model for the existing mine, which includes several attached segment conveyor belts, the researchers developed two alternative models:  with and without a surge bin. Both were used to determine the optimum design elements, such as belt 85  size, belt speed, and bin capacity. The surge bin was placed at a junction point in between the upper and downstream segments to ensure consistent flow of coal throughout the system. Loading of coal into the conveyor was represented by a random function as a coal-loading rate during simulation.  Belt spillage, breakdowns, and time between failures were included in the models.  Comparing the results of the two models, a 13.2% increase in production was expected in the optimal system with a surge bin.   Roberts (2002) studied the impact on productivity of replacing 35-t trucks with a new design of an 80-t underground haulage truck in a transverse open stoping gold mine. Fewer numbers of higher-payload trucks was the obvious solution to a queuing problem associated with a large number of 35-t trucks.  Four scenarios of existing and potential upgrades of haulage trucks for the existing and a deeper ore body were simulated. It was found that less than half of the higher-payload trucks could satisfy production demand by enlarging the existing passing bays to accommodate two 80-t trucks and increasing the spacing of passing bays in the decline.   Salama and Greberg (2012) optimized the number of load-haul-dump machines (LHDs) and trucks utilized in a haulage level in a deep sublevel open stoping mine. LHDs load material from ore production zones to loading points, then dump trucks transport material to a single shaft point.  There are seven production drifts, each one containing over 20 stopes. Three stopes can be operated at a time with only one LHD assigned to each stope. The results of Salama and Greberg (2012) indicated that by increasing the number of trucks from three to six, production performance would proportionally increase, as well as the traffic. Beyond this number, poor truck utilization is expected, due to the increase in truck waiting time. 86  3.2.2 Application of DES in Block Caving In the past, and due in part to the complexity of the block cave system and the interdependencies between construction activities, mine planners tend to rely on using conventional techniques which integrate experience from other operations and expert judgment into spreadsheet calculations (Hindle & Mwansa, 2012). Hall (2000) discussed a model prepared for PT Free Port, Indonesia, to simulate an underground block cave production system.  Mucking activities, secondary blasting in the extraction level, trucking activities in the haulage level, and material handling operations were modeled. The model was designed to obtain the best combination of loaders in the extraction level, and trucks in the haulage level that transport the material to ore passes, and then to the crusher bin. The results yielded 8 loaders and 13 trucks as the optimum fleet number.   Simulation was only recently extended to include models that simulate the development and operation of underground block cave mines (Li, 2012).  For example, Greberg and Sundqvist (2011) described a DES model prepared for the Cadia East panel cave mine.  DES tool was used to verify the development plans and to optimally allocate resources. The main problem was ensuring that the mine production could commence according to the plan. This necessitated that ventilation, conveyor belt, and panel development activities were completed on time.   Hindle and Mwansa (2012) studied a logistical problem of moving men and material into and out of the Grasberg block cave mine and, consequently, examined the interaction between the rail and shaft.  They emphasized that the primary role of the simulation was to model the 87  interdependencies between the complex infrastructures which cannot be correctly represented by spreadsheet calculations.   Simulation has been applied to mine planning and design of block caving.  A trade-off study by Labrecque et al (2012) on the final detailed design of Oyu Tolgoi (OT) was examined.  The results of the study indicated that the El Teniente design in the extraction level had more advantages in terms of drawbell construction rates than the offset Herringbone layout, although the former was less favorable in terms of production rates.  Simulation also assisted the design team in making a better decision regarding the ore pass locations and optimizing the undercut design.    Wolgram, et al. (2012) used the final infrastructure of the OT layout to estimate the long-term lateral development and mass excavation rates, in order to optimize the resource utilization and ventilation ramp up rates.  This was an application of simulation that focused on producing a schedule for lateral and mass excavation rates.  To capture the realistic schedule, it was assumed in this model that the development rates had to be reduced by 20% overall to accommodate the impacts of major fault zones and bad ground conditions on the schedule.  However, such risks should be characterized and classified in a more-explicit manner.   Such studies have demonstrated the ability of DES to model caving systems and aid mine planners in developing a base case design and schedule, and providing insight regarding how to optimize expenditures; however, still further work attention appear to be required to: 88   Offer details in how such models can be formally developed and built, what type of and how uncertainty can be characterized and integrated in these stochastic models.  Develop models that integrate the strategy of the advance undercut technique with respect to the multitasking and sequencing of the construction of drawbells and development of interrelated lateral infrastructure headings.   Develop models that examine different flexible scenarios related to the construction in which those scenarios’ results are analyzed.  3.3 Simulation Framework 3.3.1 Scope of Simulation Models The simulation models concerned emulating the development of the interconnected levels, the apex, undercut, extraction, drawpoint, and drawbell drifts, and construction of the production cells, the drawbells, and associated undercut strips, with respect to the advance undercut strategy of an existing underground caving system.  Attention is given to those essential production levels since they involve significant capital and time commitments, require multiple face headings, and are in the schedule critical path.  Access development to the ore body as well crusher excavation were not included in the models.  Key modeling assumptions are highlighted as follows:   Construction of other infrastructure components, e.g. refuge stations, storage rooms, fuel stations, explosive magazines, lunch rooms, roadways, ventilation fans, vent raises, and machine shops, are not explicitly part of the models and it is assumed that such infrastructure is available to satisfy the safety and resources requirements.  89   Ventilation capacity was assumed to be adequate and available for all equipment and manpower needs in all stages of development and construction to satisfy multiple face headings because ventilation capacity should satisfy production needs.  The maximum amount of development and construction equipment were optimized based on the constraint imposed by the advance undercut strategy and not by matching the number of open faces.  3.3.2 Distinction between Development and Construction Models The development and construction processes have been simulated through two distinct models. This distinction mimics reality since different crews, activities, equipment, and timing are scheduled for those distinct stages. The development process is referred to as the progression of sequential tunneling using the drill-and-blast technique.  The development process leads the construction process, since lateral tunneling is necessary to provide access to construction crews. Development activities involve sequential activities, drilling, blasting, mucking, and supporting drifts, and other related non-operating activities.    In contrast, construction is regarded as to as the process of constructing drawbells that connect the undercut and extraction levels. It also involves blasting undercut strips, supporting drawpoint drifts, reinforcing all intersections (bull noses and camel backs), and building underground roadways that connect draw points in the extraction level. Little interaction is expected between development and construction activities because construction of drawbells requires safe and stable ground conditions that is obtained by advancing the development and ground support ahead of time using the advanced undercut strategy.  90  3.4 Model Evolution Simulation models were established for development and construction processes and evolved from simple to complex models.  Building of those models was carried out in three distinct phases for both development and construction processes: (i) typical, (ii) comprehensive, and (iii) scenario models.  3.4.1 Evolution of Development Models The typical development models (TDM) can be used as the building block for building real case models. As shown in Figure 3.1, each activity in the single drift mining cycle required for developing those drifts within the ore body footprint was originally simulated independently and considered as initial development models (IDM). TDM is the integration of IDM to capture the complete drift mining cycle. Each TDM involved emulating several mining cycles in series while using “area gating” that allowed those drifts to be progressed one at a time in which the five sequential mining activities, and related non-operational tasks captured one complete drifting mining cycle. TDM is performed based on one development crew assigned for a specific activity. At this modeling phase, one crew consists of a single type of equipment, and it is represented by one resource pool for each activity.  This facilitates flexibility to be incorporated into multiple tasking and equipment sharing later in the subsequent phases.  91    Figure 3.1 Evolution of development models (typical, comprehensive, and scenario models)  TDM were calibrated to emulate both the temporary and permanent headings in development of the apex (TDM-EH-A), undercut (TDM-EH-U), extraction (TDM-EH-R), and drawpoint (TDM-EH-X) drives, in which no shotcreting or split set bolting are required in the temporary ground support in the case of the apex and undercut drives, while full permanent ground support is applied for extraction and crosscut drifts.  Consideration was given to the variability with respect 92  to the number of drifts required to complete one advance undercut progress cycle (AUPC). TDM has evolved further to adapt for utilizing the conveyor system instead of the truck-haul system. These models (TDM-EV-A, U, R, X), as shown in Figure 3.1, became the building block for all models employing the conveyor system. All models incorporate risk profiles for activity durations and equipment breakdowns using Beta and Weibull probability density functions to account for geotechnical and construction uncertainties.  The comprehensive development models (CDM) are those TDM which, when integrated together, emulate the actual development process of each AUPC. Each one of the CDM imitates the development process of different combinations of numbers of drifts in the apex, undercut, and extraction levels for the early and full stage of development.  In the beginning of the development, where a limited amount of open access is available, only one undercut drive, two apex drives, one extraction crosscut, and two extraction drives are integrated together to form one model (CDM-EH-2M). This model was then expanded to encompass multiple headings, as in the case of three headings in apex, two headings in undercut, three headings in extraction drifts, and two headings in crosscut drifts, which were integrated together to form one model (CDM-EH-3M).  In the same manner, this model was expanded further to capture the larger progress cycles:  four headings in apex, three headings in undercut, four headings in extraction, and three headings in crosscut models were combined to form a model that represents a progress cycle, (CDM-EH-4M). Further expansion was carried out to encompass more progress cycles, as in the case of (CDM-EH-5M), which was the state of five headings in the apex, four headings in the undercut, 93  five headings in the extraction, and four headings in the crosscut drifts are integrated. Similarly, the model (CDM-EH-6M) integrated six headings in the apex, five headings in the undercut, six headings in the extraction, and five headings in the crosscut drifts. These five models represent all possible development possibilities with the El Teniente layout design when side-sequencing in the advance undercut strategy is implemented. An illustration is given in Figure 3.2.   Figure 3.2 Side-sequencing and Middle-sequencing strategies (plan view of New Afton ore body footprint)  The scenario development models (SDM) were developed in allowing one to examine the impact of utilizing a conveyor system for each AUPC for a side-sequencing strategy for both designs of extraction layouts, as shown in Figure 3.3. As TDM models were used to develop SDM, the first scenario was to develop a model (SDM-EV) that can examine the impact of utilizing a conveyor 94  system. The second and third scenarios were to study the influence of alternating the design of the extraction layout from El Teniente to Offset Herringbone using both truck-haul and conveyor systems (SDM-OH and SDM-OV). Driven from the same modeling approach as the comprehensive development models, five models were adopted for each AUPC for each scenario as shown in Figure 3.1.  Four development crews were assumed to undertake the development activities in all accessible drifts in every AUPC.   Figure 3.3 El Teniente and Offset herringbone layout designs (plan view)  3.4.2 Evolution of Construction Models The Typical Construction Models (TCM) include models for the extraction and undercut levels independently which are the building blocks of construction models, as shown in Figure 3.4. TCM-1R simulated the construction process of only one drawbell in the extraction level, based on actual sequencing and the planned deterministic durations using the truck-haul system. This model was then improved to simulate the process of constructing two drawbells in parallel, allowing for dual tasking (TCM-2R). Similarly, TCM-1U and TCM-2U were developed for activities in one and two undercuts strips, respectively. TCM-SH-RM and TCM-UM involved 95  simulation of the construction process in building several drawbells and undercut strips progressed in parallel in the extraction and undercut levels independently. TCM-SV-RM was developed as the building block for all scenario models using the conveyor system. These models were improved by incorporating risk profiles for activity durations using the beta distribution to encompass geotechnical risks, and the Weibull distribution to include equipment shutdown risks.     Figure 3.4 Evolution of construction models (typical, comprehensive, and scenario models) 96  TCM-UM, and TCM-SH-RM models were integrated together to form a comprehensive construction models (CCM). The primary model (CCM-SH-1M) is calibrated to fit the first AUPC which was initially implemented in the early stage of construction. Since the actual construction process involves utilization of equipment for multiple tasking in the extraction and undercut levels for some activities, then resource pools for similar-type machines are created to model such behavior. This model was expanded to imitate all early and full stages of construction:  simulation of the construction of two drawbells and associated four undercut strips, (CCM-SH-2M); three drawbells and associated six undercuts, (CCM-SH-3M); four drawbells and eight undercut, the (CCM-SH-4M); and five drawbells and associated 10 undercuts, (CCM-SH-5M). Using DES and the dynamic programing technique, the number of construction machines utilized for each major construction activity was optimized for CCM-5M in which three LHD, one remote explosive machine, three long-hole drills, two cable bolting machines, and one in-the-hole Roger drill were utilized, see Appendix A.   The first scenario construction model (SCM) was developed in which one can examine the impact of utilizing the conveyor system for each AUPC for a side-sequencing strategy. Using the same modeling approach as the CCMs, five construction models were adopted for each AUPC; (SCM-SV-1M, 2M, 3M, 4M, and 5M) for a side-sequencing strategy. The second scenario construction models was developed in which one can examine the impact of altering the undercut sequencing strategy from side-sequencing to middle-sequencing using truck-haul and conveyor systems for each AUPC. See Figure 3.3. These scenario construction models with regards to truck-haul system are (SCM-LH-1M, 2M, 3M,... 10M), and with respect to the conveyor system, these models are (SCM-LV-1M, 2M, 3M,...10M).  97  3.5 Modeling Uncertainties Statistical analysis is conventionally used to model ground and equipment-related risks and uncertainties based on actual recorded data. Complete sets of construction data can be used to conduct a statistical analysis and derive an estimate that represents uncertainty in development and construction.  However, such complete construction records for geotechnical uncertainty and equipment breakdown are usually not available and a major measurement campaign needed to be conducted to gather more ideal and reliable input data. Nonetheless, for the intended purpose of this study, Beta and Weibull distributions were used based on estimated parameters to characterize uncertainty in activity durations and equipment availability. Assumptions based upon the professional experience from mining engineers in the industry (consultants and mine operators) was used to derive the estimates and parameters.  3.5.1 Geotechnical Uncertainties  The influence of rock mass characteristics uncertainty on the construction process is characterized using the Beta distribution and integrated implicitly into activity duration estimation. The implication was that geotechnical uncertainties would delay completion of activities. In terms of the forecasted delays, it should be noted that in most cases, it was considered reasonable to use triangular distributions for activity times in order to be conservative. The Beta distribution is appealing for two reasons. It is bounded so events can take place only within intervals defined by minimum and maximum values. Also, the Beta distribution does not exhibit the “fat tails” of the triangular distribution in which there would be a high probability of low or high durations.   98  Given a lower or optimistic estimate ( A ), an upper bound or pessimistic estimate ( B ), and a subjective estimate of the mode or most likely value ( D ), the PERT approximation (Cottrell, 1999) is used to compute estimates of the mean and standard deviation of a corresponding beta distribution of activity durations with shape parameters   and   as follows:  ( ) ( )E T A B A     (1)  22 1( ) ( )( ) ( )Var T B A        (2)  The shape parameters of the beta distribution can be computed as:    1( ) ( ( ) )( ( ))( )E T A E T A B E TB A Var T            (3)  ( )( )B E TE T A       (4)  3.5.2 Equipment Breakdown Uncertainty  According to Vagenas et al. (1997), theoretical probabilities (e.g., Weibell distribution) are frequently utilized to fit data related to equipment failure and maintenance.  Such data can be typically obtained from maintenance records. In the case of an unavailable complete set of reliable data, Weibell, lognormal, and exponential probability functions could also be used to estimate the frequency of downtimes of mining equipment.  Among those probability distributions, the Weibell is generally considered more versatile. It is widely used in reliability analysis, life testing, and some applications of equipment maintenance and breakdown modeling 99  (Sobral & Ferreira, 2013; Wang & Keats, 1995). In order to account for major equipment breakdowns, time-to-failure (TTF) and time-of-repair (TOR) [time between failure (TBF) and time to repair (TTR)] are required to fully characterize equipment-related uncertainties.    A two-parameter Weibull distribution was employed to simulate equipment availability for both TTF and TTR, which is explicitly integrated into the DES models.  Equipment failures are assumed to be independent of repairs, as subsequent failure begins immediately after the last failure occurred, not after the last repair was completed. The Probability Density Function (pdf) and Cumulative Density Function (cdf) that represent underground equipment failure events caused by the progression of time are given by (Wang & Keats, 1995).       1; ,tf t t e             (5)  11( ; , )tF t e        (6)  In DES models, the scale parameter   is set equal to 1 since it is assumed no breakdowns occurs early in construction. Failure model   is set equal to 1 since events are assumed to randomly fail, independent of time.  This assumption means failure rates occur constantly over time and no effects of infant mortality or aging are expected. When those parameters are equal to 1, this represents an exponential distribution.  More discussion regarding shape and scale parameters is found in Vayenas et al. (1997). All equipment is modeled at 80% availability and the location parameter is assumed to be proportionally correlated to the nature and frequency of shutdowns.    100  3.6 Typical Model Setup and Assumptions 3.6.1 Typical Development Model Build-up  In the mining cycle of single drifting, there are five major processes in one operating cycle and several non-operating non-sequential activities, as discussed by Moss (2009) and Ahmed and Dunbar (2012). The activities involved in one cycle are depicted in Figure 3.5. Non-operating activities (NOA), are non-sequential activities and can occur between any of the sequential cyclic operating activities (COA). For example, cycle preparation is an activity preceding each of the five major COA and total cycle preparation time is summed to represent the duration of this activity.  Also, equipment breakdown could happen in any stage of drifting.        Figure 3.5 (Top) sequential operating activities of a drifting cycle; (Bottom) non-sequential non-operating activities of a drifting cycle  Most simulation activities and elements are organized around specific events and interact when those specific events occur over time and are represented by DES. Simulating those activities shares the same modeling attributes in every drifting mining cycle.  In the beginning of simulation, a specific number of stopes (mining cycles) are created as items based on a schedule. An item in DES is referred to as any element that flows through the model and is processed by any specific activity required to complete a certain task. In this case, items are initially the stopes Preparing Face Drilling  Face Loading and blasting Muck heading  Ground supporting Cycle preparation Equipment breakdown Blast Re-entry Shift Change Others 101  or mining cycles. They flow through the model as being processed through the five sequential activities, in which an area gating allows only one stope to be processed at a time.    The second step occurs when each item arrives at any activity to create sub-items specifically for each activity m  based on the required scope of work mQ  and, thus, the quantity of sub-items is calculated accordingly.  For example, items can be the number of truck loads to be hauled to surface, square meters of shotcrete to be placed on the face and the back of the drift, resin bolts to be installed and support the rock mass, or holes to be drilled and blasted into the face. Before being processed, sub-items gather into a stored queue entry that allows each one to be processed independently. Activity block processes every sub-item based on the required number of recourses mE  to perform any particular task. The scope of work mQ  is used to calculate the activity duration mT based on productivity of the work mP  and resource usage mE  as shown in Equation 7 (Hendrickson et al., 1987). Activity durations mT  estimated for sub-items are shown in Table 3.1. More discussion is given in section 3.6.2  mm m mQT P E  (7) Major development equipment are modeled explicitly as “resource pools,” since each piece of equipment modeled in a resource pool performs a specific task. Each development crew consists of a drilling jumbo, an emulsion loader, a concrete mixer, a shotcrete sprayer, a scoop, and two trucks. One resource pool may contain equipment that are utilized in multiple drifts.  Typical equipment used in the development of the New Afton mine are presented in Table 3.2. When a sub-item arrives to an activity block, its related equipment leaves the “resource pool” and is 102  assigned to this activity until the work is completed, then this machine returns to its resource pool.  Several identical machines are shared among multiple drifts and whenever the item is ready to be processed, a free one is assigned to it on a first-come-first-served (FCFS) basis. Equipment shutdowns are modeled implicitly based on the Weibull distribution.  After a complete activity is performed, its sub-items are returned (batched) to the original item and flow to the next activity, where different tasks and progress rates are required.  A mining cycle in the typical models is accomplished when all activities are completed.  Table 3.1 Input modeling parameter of one development mining cycle  Activity Task Sub-Items in Queue Ahours/ item D  hours/ item B  hours/ item Mean duration µ𝑡  hours/ item Standard dev. 𝜎𝑡 hours/ item (1) Mucking 1.1 Ore mucking 8 0.25 0.25 0.30 0.258 0.00833 1.2 Truck hauling 2 1.50 1.50 1.50 1.50 0 (2) Shotcreting 2.1 Geo-tech inspecting 1 0.33 0.33 0.33 0.33 0 2.2 Preparing 1 0.43 0.43 0.43 0.43 0 2.3 Hydro-scaling 1 0.20 0.20 0.20 0.20 0 2.4 Mixing 2 0.5 0.5 0.50 0.50 0 2.5 Shotcreting 84 0.0075 0.0075 0.0113 0.008 0.00063 (3) Bolting 3.1 Bolting preparing 4 0.33 0.33 0.33 0.33 0 3.2 Resin bolting 4 0.63 0.63 0.78 0.655 0.025 3.3 Face scaling & cleaning 4 0.66 0.66 0.66 0.66 0 (4) Drilling 4.1 Drilling preparing 1 0.33 0.33 0.33 0.33 0 4.2 Face surveying 1 0.15 0.15 0.15 0.15 0 4.3 Hole drilling 264 0.0073 0.0073 0.0083 0.007 0.00017 (5) Blasting 5.1 Charging preparing 1 0.25 0.25 0.25 0.25 0 5.2 Loading 1 1.50 1.50 2.00 1.583 0.00694 5.3 Blasting & shift change End-of-shift blasting  1 0.66 0.66 0.66 0.66 0      103  Table 3.2 Major equipment utilized in development  Activity Task Equipment (1) Mucking 1.1 Ore mucking 7 yard Cat R1600; 10 yard Atlas Copco Scoops 1.2 Truck hauling 45 ton Cat AD 45; 50 ton Atlas Copco Trucks (2) Shotcreting 2.1 Geotechnical inspecting General Utility Equipment 2.2 Shotcrete preparing General Utility Equipment 2.3 Hydro-scaling General Utility Equipment 2.4 Mixing 4 𝑚3 Marcotte; 6  𝑚3 Normet Transmixers 2.5 Shotcreting Normet Sprayers (3) Bolting 3.1 Bolting preparing General Utility Equipment 3.2 Rasin bolting Sandvik; Atlas Copco Bolters 3.3 Face scaling & cleaning General Utility Equipment (4) Drilling 4.1 Drilling preparing General Utility Equipment 4.2 Face surveying General Utility Equipment 4.3 Hole drilling Sandvik; Atlas Copco Jumbo drills (5) Blasting 5.1 Charging preparing General Utility Equipment 5.2 Loading MineCat Emulsion Loader 5.3 Blasting & shift change (End-of-shift blasting ) General Utility Equipment  3.6.2 Development Model Activities Input Parameters   All development activities are modeled based on how they are exactly performed in the mine. Detailed input parameters for typical models are discussed below.   Ore mucking.  The apex, undercut, and extraction drifts are 4.2 m wide x 4.2 m high, and haulage is 5.0 m wide x 5.5 m height. Each mining cycle is assumed to be 4.0 m long.  Rock mass rating (RMR76) values range approximately between 31 (very weak) to 45 (weak) (New Gold, 2012). It is assumed that at the end of every cycle when end-of-shift blasting has been undertaken and the crew shift changes, the mucking activity commences in all blasted drifts as 7 to 10-yard scoops (LHD) and 45-t and 50-t trucks are responsible to muck approximately 190 to 200 tonnes of ore to surface. It is assumed that a uniform integer 8 “truck load” items must be hauled to surface. An average 50% bucket factor is expected in every truck.  However, the quantities of mucking are random variables and are depicted from the blasting quality of 104  previous activities.  Moreover, good blasting comes with higher RMR76 and vice versa.  Lower RMR76 values provokes over breaks and translates into 5% extra muck. Beta distribution is assumed to characterize the stochastic nature of ore mucking activity, as 20% delays are expected.   Shotcreting. To immediately support the back of the horizontal drifts and ensure a safer work environment, fiber reinforcement shotcrete (FRS) is frequently implemented immediately after mucking is completed.  The design of the extraction level required minimum thicknesses of 70 mm and 100 mm of shotcrete used in the extraction and drawpoint drifts, respectively, and an additional 50 mm high strength SFRS applied to bull nose for wear protection.  Due to the current state of a weaker rock mass, the construction team applied 100 mm and 150 mm for the entire mine development based on the two categories of rock (very poor and poor ground). To characterize uncertainty in rock mass characteristics, it is assumed that the scope of work   is the total number of square meters of concrete required to support the drift based on the tunnel face and back surface area of 84 m2 (items).  In ideal equipment and ground conditions, shotcreting can be implemented at a rate of 4.8 min/m3 (0.21m3/min). Weaker RMR76 entails extra time to shotcrete and that is characterized in a pessimistic value of the beta distribution.    Concrete is batched and mixed up on surface and then transported to the footprint using slickline. Slickline is a pipe approximately 600 m long and 15.2 cm in diameter. Based on the capacity of the batching plant on surface, it is assumed that from 60 to 70 m3 of concrete can be used in twelve-hour shift. It is assumed also that a single transmixer can feed a shotcreter (spraymec) with 4 to 6 m3 of concrete and will take 30 min of remixing and transporting each load. Other 105  activities prior to shotcreting such as geotechnical inspection, shotcrete preparation, and hydro-scaling are integrated into the simulation. It is assumed that no shortage of concrete is expected during shotcreting and supply is always available for demanded drifts.    Rock bolting. Rock bolting is used to complete the process of permanent rock support and ensure lifelong mine ground support.  Split set or resin rebar bolts are typically used to support a weak rock mass.  In a 4 m mining cycle, four rings are installed. Each one has either 9 or 11 bolts per ring, depending on the rock mass conditions to support the back and sides of the drift.  Those two extra resin bolts are used only in very poor rock masses. Each bolt is, approximately 2.1 m long, takes an average of 1.8 min to drill and 2.5 min to install.  Prior and subsequent activities such as bolting preparation, as well as scaling and cleaning, takes 20 min and 40 min on average respectively, to complete this task.  One bolter equipment is utilized to perform rock bolting. In extremely weak rock mass, cable bolting is used to support the drift; however, only the construction model that the cable bolting is applied to supports all intersections. Normally in this case, mining cycle takes nearly double the time, given that more mucking and ground support are required.    Face drilling and blasting. Face drilling and blasting are the last activities to complete the cycle. Face preparation and surveying activities precede face drilling using a duel-boom jumbo face rig to guarantee quality drilling.  It is assumed that 66 drill holes along the face must be drilled in every cycle at an average penetration rate of 2.28 m/min and in the worst case situation, it takes 2.0 m/min in poor working conditions.  Loading and blasting are the last activities in the cycle and must be done at end of one’s shift.  An emulation loader with platform 106  and boom lift is used to manually load holes with explosives.  After blasting, safety regulations require that time is dedicated to ventilating the drift free of any residuals of blasting before starting the next cycle.  All models are standardized, in which blasting preparation, charging, and blasting as well as shift changing are always conducted at the end of a shift.  It is assumed that 40 min is the time required for ventilating a drift.   3.6.3 Typical Construction Model Build-up Construction crews, on the other hand, start working independently in the undercut and extraction levels, lagging the development crews. Distinguished from the development mining cycle, one construction progress cycle consists of drilling and blasting of several undercut strips, and building associated drawbells depending on the width of the ore body at any particular location. For example, building five drawbells in the distressed zone requires 10 undercut strips to be blasted above the extraction level.  An active progress cycle must be completed before advancing to the next one. It is expected to have five smaller progress cycles starting from the building one drawbell and associated two undercut strips in the initial cycle to arrive at the largest progress cycle in, which five drawbells are constructed in one cycle, since the width of the ore body encompasses five drawbells in one row.   Construction activities are performed in which parallel or sequential arrangements link them together based on the logic between them. All activities are scheduled based on the finish-to-start algorithm, as shown in Table 3.3.  Five shared resource pools are created to model the five major equipment types employed in the construction of drawbells and two shared resource pools are created for undercut work since only two type of equipment used for undercutting.  Pieces of 107  equipment used for long-hole drilling and blasting activities are shared between the undercut and extraction activates; however, other equipment is dedicated only to extraction level construction, as presented in Table 3.4. Similar to development models, uncertainties in rock mass and construction equipment are characterized using Beta and Weibull distributions as means of representing activity duration and equipment shutdown uncertainties.  Table 3.3 Input modeling parameters of a typical drawbell construction  Activity (sub-item) OPT Adays ML Ddays PES Bdays Predecessor  Successor  Beta   Beta   Meanµ𝑡  Stand. Dev. 𝜎𝑡 (1) Roger raise boring 3.5 3.5 4.0 DVL ACT (2) 0.67 3.33 3.58 0.08 (2) Cable bolting DP1 3.5 4.0 5.0 ACT (1) ACT (3,4) 7.10 11.15 4.08 0.17 (3) Pedestal installation 1.5 1.5 2.0 ACT (2) ACT (5) 0.67 3.33 1.58 0.08 (4) Cable bolting DP2 3.5 4.0 5.0 ACT (2) ACT (6,7) 7.10 11.15 4.08 0.17 (5) Steel set installation DP1 3.0 3.0 4.0 ACT (3) ACT (7) 0.67 3.33 3.17 0.17 (6) Concrete floor pouring DP2 1.5 1.5 2.0 ACT (4) ACT (8) 0.67 3.33 1.58 0.08 (7) Drawbell drilling 4.0 5.0 6.0 ACT (4,5) ACT (9) 17.5 17.50 5.00 0.17 (8) Steel set installation DP2 3.0 3.0 4.0 ACT (6) ACT (10) 0.67 3.33 3.17 0.17 (9) Concrete floor pouring DP1 1.5 1.5 2.0 ACT (7) ACT (10) 0.67 3.33 1.58 0.08 (10) Drawbell blasting 0.5 1.0 1.5 ACT (8,9) ACT (11) 17.5 17.5 1.00 0.08 (11) Drawbell mucking 10.0 10.0 12.0 ACT (10) FIN 0.67 3.33 10.30 0.33 (OPT) optimistic - (PES) pessimistic - (DP) drawpoint face - (DVL) development - (ACT) activity - (FIN) finish  Table 3.4 Major equipment used in construction  Activity Equipment (1) Raise boring In the hole Roger Machine (2) Cable bolting DP1 Tamrock DS-310 Bolter (3) Pedestal installation General Utility Equipment  (4) Cable bolting DP2 Tamrock DS-310 Bolter (5) Steel set installation DP1 General Utility Equipment (6) Concrete floor pouring DP2 Utility Equipment (CAT grader, compactor, and skidsteer) (7) Drawbell drilling Sandvik Longhole drills (8) Steel set installation DP2 Utility Equipment (9) Concrete floor pouring DP1 Utility Equipment (CAT grader, compactor, and skidsteer) (10) Drawbell blasting Remote Long hole loading machine (Always end-of-shift blasting ) (11) Drawbell mucking 45 ton Cat AD 45; 50 ton Atlas Copco Trucks 7 yard Cat R1600; 10 yard Atlas Copco Scoops  108  3.7 Comprehensive Model Assumptions CDM are those models that emulate the process of building the interdependent lateral infrastructure levels within the footprint for every AUPC. Based on reality, it is assumed that all development crews advance simultaneously in all levels, apex, undercut, and extraction levels, in order to achieve the target development rates. The development of the apex, undercut and extraction drives are coupled with the development of extraction drawpoint drives, as depicted in each unique working zone in advance undercut strategy. To achieve higher development rates, the El Teniente layout style is considered and, thus, the development of the straight-through extraction crosscut drives becomes a major component in those models.    Five AUPC were developed to emulate the early and full scale of development in which the progress of development from a limited number of attainable open drifts to maximum allowable  number of drifts are considered, as shown in Figure 3.6. The first progress cycle involves developing one extraction crosscut that can be accessed from either side of the extraction drives, one undercut drift, and two associated upper-level apex drives. Then the second progress cycle involves two extraction crosscuts and undercut drives, and three extraction and apex drives. In the same manner, attributes and characteristics of larger cycles are modeled.  The largest progress cycle includes five neighbors of crosscuts, six extraction, five undercut, and six apex drives.109   Figure 3.6 Advance undercut progress cycles - early stage of construction ramp-up (plan view) 110  Construction crews start working simultaneously in the undercut and extraction levels, lagging the development crews to achieve the target construction rates. Construction advances when ventilation is fully applied in developed construction areas. Construction equipment are shared based on machine availability and activity schedule between undercut and extraction until undercut work is completed, then, equipment is dedicated to extraction level until the AUPC is completed. Five shared resource pools are used in the simulation for undercut and extraction construction crews, and the number of equipment in each pool is optimized to achieve maximum construction performance.    The goal is to build approximately four new drawbells every month in full-scale construction. CCM were built to capture the early and full stages construction. The first CCM imitates the process of building the first drawbell in the extraction level coupled with the first two undercut strips in the undercut level, and, similarly, it is assumed for the second, third, and forth AUPC of the early stages of construction and the fifth AUPC in full-stage construction. An active AUPC must be completed before advancing to the next one, as a way to ensure proper undercut blasting is created.   In every AUPC, development and construction requirements were determined based on the permissible number of drifts and associated meters of heading per drift, and number drawbells and undercut strips to be constructed in this cycle. The number of development meters is based on four-meter development cycles in all levels. The number of drifts, development cycles, and meters of headings in each level vary from one location to another. The scope of work required for development and construction in each AUPC is presented Table 3.5. The scope of work in 111  any AUPC must be achieved before moving ahead to the next cycle.  Therefore, the total duration of one cycle is depicted by the longest duration of those four components (infrastructure levels) in the different development stages.   Table 3.5 Development requirements for every comprehensive development model Development Scope Requirements Apex  drive Undercut drive Extraction drives Extraction crosscuts Primary Model  Infrastructure drifts 2 1 2 1 Mining cycles 9 5 9 7 Development  meters  36 20 36 28 Drawbells 0 0 0 1 Undercut Strips 0 2 0 0 Twin      Model Infrastructure drifts 3 2 3 2 Mining cycles 13 9 13 13 Development  meters  52 36 52 52 Drawbells 0 0 0 2 Undercut Strips 0 4 0 0 Tertiary Model  Infrastructure drifts 4 3 4 3 Mining cycles 17 13 17 20 Development  meters  68 52 68 80 Drawbells 0 0 0 3 Undercut Strips 0 6 0 0 Quaternary Model   Infrastructure drifts 5 4 5  4 Mining cycles 21 17 21 27 Development  meters  84 68 84 108 Drawbells 0 0 0 4 Undercut Strips 0 8 0 0 Quinary Model  Infrastructure drifts 6 5 6 5 Mining cycles 25 21 25 33 Development  meters  100 84 100 132 Drawbells 0 0 0 5 Undercut Strips 0 10 0 0   3.8 The Benchmark Model Assumptions The benchmark model scenario (Scenario-ESH) is a combination of several CDM and CCM which emulate the entire development and construction of the Blocks 1, 2, and 3 of the mine. This required integrating of all AUPC in the early, middle, and later stages of development and 112  construction. Scenario-ESH is attributed by side-sequencing utilizing truck-haul system since the mine undercut face was originally initiated from the north-west side of the ore body footprint and advanced to the west. This scenario encompasses 49 AUPC as shown in Figures 3.7 and 3.8. This assumption is made by determining the number of allowable access to drawbells in early and full stages of construction as the mine advances from the east to west direction. As the mine decided to extract the high grade ore first, Block 2 (the middle block in Figure 3.2) will be reserved as a major pillar between Block 1 and Block 3 until construction for those blocks is completed, then it will be constructed last.    Figure 3.7 Number of drawbells constructed in every AUPC for side-sequencing scenarios  Block-1 Block-3 Block-20123451 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49Construction (drawbell open access)Advance undercut progress cycle113   Figure 3.8 Advance undercut progress cycles for side-sequencing scenarios – subsequent AUPC shown in different color (plan view)  3.9 Scenario Model Assumptions The first scenario (Scenario-ESC) was modeled to utilize the transportation blasted rock from all drifts in all levels as well as blasted drawbells using a conveyer belt rather than transporting the ore using a truck haulage system. Similar to the benchmark model, 49 AUPC are considered utilizing a side-sequencing strategy. It is assumed that the ore passes, haulage drifts, gyratory crusher, and conveyor are available to be used in this early stage of development. Despite the fact that scenarios can be built by alternating between the truck-haul and conveyor systems for the entire mine, no alternation is assumed to occur between those two systems during the process of any progress cycle. The entire AUPC can be performed completely by either one of those systems.    It is assumed that the actual duration of mucking activity using the conveyor includes the time from loading at drawpoints, travelling and dumping to ore passes. The conveying time has not been modeled despite the fact that the broken rock is required to travel 4,530 meters on a four-114  leg conveyor belt to reach the surface at a speed of 2.4 m/s (8.64 Km/h), which roughly takes 31 min travel time. It is assumed that any time between 4 and 5 minutes is the time required to move ore from one stope to the nearest ore pass in one direction (average 9 min total travel time for one load). Since the conveyer belt is designed to move high production capacity, no congestion is expected and ore should be smoothly transports to the surface.   The second scenario models (Scenario-OSH and Scenario-OSV) were modeled to capture those smaller cycles determined by the additional turnouts of the Offset Herringbone layout design using both ore handling systems. As opposed to the six 4-meter full drifting mining cycles modeled in El Teniente layout in drawpoint drifts, development of extraction crosscut drifts in Offset Herringbone are simulated sequentially in three stages. First, two 4-meter mining cycles from one side of a drawpoint drift are undertaken, followed by four smaller 2.5-meter cycles in drawbell drift.  Then, the last two 4-meter full mining cycles are conducted from the other side of drawpoint drifts to finish up this crosscut drift.  Activity durations of smaller drifts are assumed to be reduced by up to 62.5 % of the typical duration for COA.  NOA is assumed to be similar in both extraction styles, since preparation and other non-operating activities should not change. Development of apex, undercut, and extraction drifts are assumed to be the same for both cases.   The third scenario models (Scenario-ELH and Scenario-ELV) were built to examine the impact of altering the undercut sequencing strategy from side- to middle-sequencing, utilizing the truck-haul and conveyor systems respectively.  In these models, up to 10 drawbells and associated 20 undercut strips can be constructed in one AUPC from both undercut faces, 25 AUPC are considered utilizing middle-sequencing strategy as shown in Figures 3.9 and 3.10. It is assumed 115  that construction is physically constrained by the availability of open faces in an active construction zone associated with the advance undercut strategy.    Figure 3.9 Number of drawbells constructed in every AUPC for middle-sequencing scenarios   Figure 3.10 Advance undercut progress cycles for middle-sequencing scenarios – subsequent AUPC shown in different color (plan view)  0123456789101 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Construction (drawbell open access)Advance undercut progress cycle116  In conclusion, the scenarios undertaken are as follows:  Scenario-ESH:  1) EL Teniente, 2) side-sequencing, and 3) truck-haul system   Scenario-ESV: 1) EL Teniente, 2) side-sequencing, and 3) conveyor system  Scenario-OSH: 1) Offset Herringbone, 2) side-sequencing, and 3) truck-haul system   Scenario-OSV: 1) Offset Herringbone,2) side-sequencing, and 3) conveyor system  Scenario-ELH: 1) EL Teniente, 2) middle-sequencing, and 3) truck-haul system  Scenario-ELV: 1) EL Teniente, 2) middle-sequencing, and 3) conveyor system  Moreover, two cases were considered for both Scenario-ELH and Scenario-ELV:   Case 1:  The number of construction machines utilized in middle-sequencing for each major activity is assumed to be similar to the optimized number of equipment employed for benchmark model Scenario-ESH, in which three LHD, one remote explosive loader, three long-hole drills, two cable bolting machines, and one in-the-hole Roger drill are utilized.   Case 2:  The number of construction machines utilized in middle-sequencing for each major activity is selected based on the dynamic programing (DP) optimization method armed with DES technique in which three LHD, one remote explosive loader, five long-hole drills, three cable bolting machines, and one in-the-hole Roger drill are found to be the maximum optimal machines utilized.   3.10 Model Verification and Validation Simulation models are developed to aid the investigation and quantification of different alternatives and options that potentially can increase the economic value of a mining project.  117  These models are not intended to be utilized in daily mine planning; however, their level of detail, in terms of activity durations and statistics of variability, is calibrated to match the overall monthly actual development dates and target rates.   3.10.1 Simulation Model Verification Model verification was concerned with testing the model for software and modeling errors that could lead to misleading results.  Verification by animation or visualization, as discussed by Luckko and Rojas, (2010) and Sargent (2005) was used to verify the models. The use of the special-purpose DES commercial tool resulted in having few software errors that otherwise might have required intensive debugging. The models were tested for the absolute quantity and logic of items in every activity. As each model moves through time, the operational behavior of the items in transportation from one activity to another is displayed graphically. In the case of modeling errors, such as misplaced relationships between activities, erroneous routing of items through the models, incorrect resource capacity or type in a particular task, or absence of an activity block, graphical display of the models through time was used to find errors.   3.10.2 Simulation Model Validation The mine development models capture the actual development rates. Comparisons were made between the system's behavior and the model’s predictions as part of the validation process. Predictive validation is discussed further by Luckko and Rojas (2010) and Sargent (2005). Actual performance of the mine development in terms of the monthly average development meters were observed and used in the validation process. In the case study, the mine had utilized its own equipment and employed specialized development contractors to enable a total of four 118  development crews to be utilized in the pre-production phase. The models were validated through the results obtained for full-scale development that were realized in year 2012. An average of 793 meters of development per month was simulated, compared to 844 obtained by the mine in that period. The simulation models were effective in predicting the actual development rates to within an average of 6.17%. Cumulative plots indicate a reasonably consistent trend between actual performance and simulation, see Figure 3.11.    Figure 3.11 Comparison of actual development performance with development models  010002000300040005000600001.01.2012 31.01.2012 01.03.2012 31.03.2012 30.04.2012 30.05.2012 29.06.2012 29.07.2012 28.08.2012Construction (drawbells)Dates Truck-Haul system (development rates) New Afton underground development in 2012New Afton (6 months cumulative deveopment)Truck-Haul system (cumulative development)119  The actual and simulated start-up and full-scale construction phases of Block 1 are depicted in Figure 3.12.  The construction on the extraction level commenced in August 2011, following the development that had begun a few months earlier. Only one mining face is assumed to be accessible at the beginning of the construction, allowing the first drawbell to be constructed in September, 2011. After that, a limited number of headings were available, allowing for simultaneous construction exercises starting from two and then three drawbell per progress cycle. After building eight drawbells, full access to newer drawbells allowed construction to advance at full capacity. Four or five drawbells per progress cycle were needed to be built, depending on the width of the mine footprint at that particular area, advancing from the west to east longitudinally, until 65 drawbells were completed. The model results are shown in Figure 3.12 of the "Hybrid case," where both ore handling systems were integrated and validated against the actual performance.  Also, individual cases where the truck-haul or conveyer system are independently simulated for the entire construction are shown.  Simulation results are consistent with those figures obtained from the mine.  The construction models revealed that 130 days (4.33 months), 518 days (17.26 months), and 648 days (21.59 months) are required to complete the ramp-up phase, the full-scale phase, the Block 1, compared to 139 days (4.63 months), 464 days (15.47 months), and 603 days (20.10 months) acquired from the mine.  With respect to the start-up phase, the average construction rates obtained from simulation and the actual mine data are 1.85 and 1.73 DB/month, respectively. The average rates for the full-scale phase are 3.30 DB/month from simulation and 3.69 DB/month obtained from the mine. The average of the entire simulated construction rate is 3.01 DB/month, compared to an actual rate of 3.23 DB/month that is obtained for the actual mine. Simulation models 120  overestimate the construction start-up rate by 7.05%, while they underestimated the full-scale rate by10.39%. The variation between the models and actual entire construction rates was 6.89%, in which simulation was below the actual by 45 days (1.5 months).  Most likely the cause of the differences between the simulation and actual figures are due to the assumed probability distributions activity duration and equipment utilization input parameters.     Figure 3.12 Comparison of actual construction performance with construction models   01020304050607006/06/2011 04/10/2011 01/02/2012 31/05/2012 28/09/2012 26/01/2013 26/05/2013Construction (drawbells)Dates New Afton (actual drawbells completed)Truck-Haul system (simulation)Conveyer system (simulation)Hybrid (Truck-Haul & Conveyer starts after 29 jan 2013)121  3.11 Simulation Results 3.11.1 Optimal Equipment Operation Using Dynamic Programming Development and construction rates are critically dependent on the number of machines utilized.  Thus, the dynamic programming (DP) optimization technique and DES were used to obtain the optimal number of equipment utilized that maximize construction the construction rate. Five major equipment types are utilized to complete the construction work in the extraction and undercut levels.  Models CCM-SH-4M and CCM-SH-5M, or SEM-LH-10M were used, since the largest progress cycle involves building either four or five, and ten drawbells in side and middle sequencing strategies, respectively. Because machine types are dedicated to their relevant activity types in which a specific resource pool is used to model each machine type, the optimal number of machines in each pool is independently optimized to suit the requirements of associated activities. Results from DP are compared to the actual number of machines operated by the mine to aid the model-validation process.  Discussion of DP and results are provided in Appendix A.  3.11.2 Benchmark Model Results  The development models considered developing the three major lateral levels comprised of Blocks 1, 2, and 3, using an advance undercut strategy. Simulation results indicated that the development of extraction crosscuts were the schedule-critical paths among the three infrastructure levels in El Teniente models, despite the fact that the requirements of drifting in a smaller progress cycle (e.g., AUPC-1) differs from the larger ones (e.g., AUPC-5).  For example, in the AUPC-1 model, the apex and extraction drives require more development meters than the undercut and drawpoint drives, thus, this progress cycle is completed when the extraction 122  crosscuts are completed, see Figure 3.13.  In contrast, drawpoint and drawbell drifts or crosscut drives require more development cycles in the bigger models, such as the AUPC-3, AUPC-4, and AUPC-5, models. For example, as shown in Figure 3.14, the crosscuts are the critical path in an El Teniente AUPC-5 model, in which 33 cycles are required to complete the crosscut, compared to 25 for the extraction and apex drives, and 21 for the undercut drives. Simulation results are presented in Appendix B.    Figure 3.13 Completion times for one progress cycle requirement in the CDM-EH-2M model - one random simulation run for AUPC-1  01234567890 20 40 60 80 100 120 140 160 180 200 220Completed develepment cycles Time (Hours)El Teniente (crosscuts)EL Teniente (apex)El Teniente (extraction)El Teniente (undercut)123   Figure 3.14 Completion times for one progress cycle requirement in model (CDM-EH-6M) - one random simulation run for AUPC-5  On the other hand, with respect to construction models, in the worst case situation, when utilizing the truck-haul system for 10-day mucking in AUPC-5, 54 days (1.8 months) is required to complete this cycle as shown in Figure 3.15, or in other means, the drawbell construction rate is 2.7 DB/month. The duration required to complete the undercut for this particular cycle is 23.9 days (0.79 month). In the case of utilizing the truck-haul system for five-day mucking, the 036912151821242730330 50 100 150 200 250 300 350 400Completed develepment cycles Time (hours) Extraction CrosscutsApex drivesExtraction drivesUndercut drives124  drawbell construction rate has increased to 3.2 DB/month where five drawbells and associated 10 undercut strips are completed in 46.1 days (1.53 months) and 24.4 days (0.81 month), respectively. Despite the fact that construction models are highly sensitive to mucking strategies in which approximately 15 % is the difference between the both cases, both undercut-related activities reveal approximately the same results, since no mucking is required for undercut development.    Figure 3.15 Completion times for full-construction phase requirements in one progress cycle (one random simulation run for CCM-SH-5M)  Both development and construction model results indicate that construction of drawbells is indeed the critical path, as shown in Figure 3.16. The entire construction phase, which includes construction of 189 drawbells and blasting of 378 undercut strips, is expected to be accomplished in 66.3 months (5.53 years), whereas the entire development of 16,264 advance meters in the apex, undercut, and extraction levels are expected to be completed within an average of 18.4 0123456789100 5 10 15 20 25 30 35 40 45 50 55Construction (units)Model simulation (days)DrawbellsUndercut Strips125  months (1.53 years), which is slightly less than 30% of the entire process.  Nearly 90 active drawpoints can potentially provide 11,000 tpd at full production capacity. This production target can be initially fulfilled entirely from active drawbells in Block 1, where the production ramp-up phase requires constructing 47 drawbells, and that can be achieved after completing 12 undercut progress cycles in 16.4 months (1.37 years).  In that sense, it is significant to focus on accelerating those first 12 AUPC constituting the production ramp-up phase that aids in fulfilling production capacity, which is comprised of four early stages of cycles, followed by eight full-stage AUPC.  Figure 3.16 Simulation results for the development and construction models (Scenario-ESH) 0204060801001201401601802000200040006000800010000120001400016000180000 200 400 600 800 1000 1200 1400 1600 1800 2000Construction (drawbells)Development (meters)Model simualtion (days)full production at 47 DBEl Teniente style development (Truck-haul system)Side-sequencing Construction (Truck-haul system)126  Statistical results obtained for Blocks 1, 2, and 3 are presented in Tables 3.6 and 3.7. The combination of the results obtained for those blocks establish the total mine progress. Output results are described based on beta probability distribution, in which the first two statistical moments (the mean and standard deviation) and the optimistic and pessimistic values obtained from the simulations are used to calculate the two shape parameters of the resultant beta function. The beta cumulative density function (CDF) and probability density function (PDF) results are depicted in Figures 3.17 and 3.18 for the development and construction models.    Table 3.6 Simulation results for the development model (Scenario-ESH)  Development Model Scenario-ESH Scope of Develop-ment (meters) Statistical results Mean µ𝑡  (days) Var. (days2) Stand. Dev. 𝜎𝑡 (days) OPT A (days) PES B (days) Beta   Beta   Block 1 16 AUPCs 5,548 189.6 2.2 1.5 180.3 199.3 19.14 19.96 Block 2 8 AUPCs 2,448 82.0 1.4 1.2 77.7 88.7 7.43 11.58 Block 3 25 AUPCs 8,268 282.3 3.6 1.9 270.0 300.5 24.61 36.41 Total 49 AUPCs 16,264 552.9 7.1 2.7 528.0 588.0 49.34 69.55  Table 3.7 Simulation results for the construction model (Scenario-ESH) Construction Model Scenario-ESH Scope of Develop-ment (meters) Statistical results Mean µ𝑡  (days) Var. (days2) Stand. Dev. 𝜎𝑡 (days) OPT A (days) PES B (days) Beta   Beta   Block 1 16 AUPCs 65 666.7 6.2 2.5 651.7 681.7 17.50 17.50 Block 2 8 AUPCs 28 308.2 5.1 2.3 297.7 314.0 6.77 3.74 Block 3 25 AUPCs 96 1013.7 15.8 4.0 979.4 1035.8 28.20 18.17 Total 49 AUPCs 189 1988.7 27.1 5.2 1928.8 2031.5 54.72 39.10  127   Figure 3.17 Beta PDF and CDF for the development model (Scenario-ESH)   Figure 3.18 Beta PDF and CDF for the construction model (Scenario-ESH)   0%5%10%15%20%25%30%35%40%45%0%10%20%30%40%50%60%70%80%90%100%525 532 539 546 553 560 567 574 581 588 595ProbabilityConfidence level Duration (days)BETA CDFBETA PDF0%5%10%15%20%25%30%35%40%0%10%20%30%40%50%60%70%80%90%100%1920 1940 1960 1980 2000 2020 2040ProbabilityConfidence level Duration (days)BETA CDFBEAT PDF128  3.11.3 Flexibility in Ore Handling System Results Development and construction model results indicated that developing the ore handling system early in the construction phase adds significant improvement in the construction speed and development advance rates. Given the fact that each drawbell requires an average of 5,400 tonnes to be removed and transported to the surface to initiate caving, utilizing the conveyer drift improved the duration immensely. Moreover, the accumulated time to transport an average of 170 tonnes of ore from each four-meter cycle of drifting in apex, undercut, drawpoint, and extraction drives using the conveyor system improved the development process.   It is expected to develop 16,264 meters of drifting in an average of 408.5 days (13.62 months) employing the conveyor system, compared to 552.9 days (18.43 months) employing the truck-haul system, as depicted in Figure 3.19 and Table 3.8. Likewise, 1,676.3 days (55.87 months) is what it takes to construct 189 drawbells and associated 378 undercut strips employing the conveyor system, compared to 1,988.7 days (66.29 months) using the truck-haul system, as shown in Figure 3.20 and Table 3.9.  The worst case situation, when 10-day mucking is required for one drawbell, results in 2,340 days (78.0 months) of construction, or approximately 351 days (11.7 months) expected delay. Beta PDF and CDF and its parameters for the entire development and construction phase are illustrated in Figures 3.21 and 3.22.      129  Table 3.8 Simulation results for the development model (Scenario-ESV) Development Model Scenario-ESV Scope of Develop-ment (meters) Statistical results Mean µ𝑡  (days) Var. (days2) Stand. Dev. 𝜎𝑡 (days) OPT A (days) PES B (days) Beta   Beta   Block 1 16 AUPCs 5,548 135.9 2.4 1.5 127.3 143.3 14.66 12.62 Block 2 8 AUPCs 2,448 64.2 1.1 1.1 67.2 1.1 7.06 148.39 Block 3 25 AUPCs 8,268 208.4 4.3 2.1 194.5 220.0 19.39 16.18 Total 49 AUPCs 16,264 408.5 7.8 2.8 382.5 430.5 38.98 32.9  Table 3.9 Simulation results for the construction model (Scenario-ESV) Construction Model Scenario-ESV Scope of Develop-ment (meters) Statistical results Mean µ𝑡  (days) Var. (days2) Stand. Dev. 𝜎𝑡 (days) OPT A (days) PES B (days) Beta   Beta   Block 1 16 AUPCs 65 569.2 3.6 1.9 560.3 581.8 12.45 17.62 Block 2 8 AUPCs 28 255.1 2.7 1.6 250.9 261.9 3.88 6.28 Block 3 25 AUPCs 96 852.0 8.1 2.9 838.1 874.1 13.72 21.81 Total 49 AUPCs 189 1676.3 14.4 3.8 1649.3 1717.8 30.19 46.41  130   Figure 3.19 Comparison between simulation results for the development models (Scenario-ESH verse Scenario-ESV)  - 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,0000 60 120 180 240 300 360 420 480 540Development (meters advanced)Model simulation (days) Benchmark model (Truck-Haul system)Flexible model (Conveyer system)131   Figure 3.20 Comparison between simulation results for the construction models (Scenario-ESH verse Scenario-ESV)  0204060801001201401601802000 10 20 30 40 50 60 70 80Construction (drawbells)Model simulation (months) Construction model (truck-haulsystem) - 10 days muckingConstruction model (truck-haulsystem) - 5 days muckingConstruction model (conveyorsystem)132   Figure 3.21 Beta PDF and CDF for the development model (Scenario-ESV)   Figure 3.22 Beta PDF and CDF for the construction model (Scenario-ESV)  The entire mine development schedule is reduced by 4.8 months (26.2 %), or in other words, the performance has improved by a rate of 312 development m/month, as shown in Tables 3.10 and 0%5%10%15%20%25%30%35%0%10%20%30%40%50%60%70%80%90%100%378 385 392 399 406 413 420 427 434ProbabilityConfidence level Duration (days)BETA CDFBETA PDF0%5%10%15%20%25%30%35%0%10%20%30%40%50%60%70%80%90%100%1640 1650 1660 1670 1680 1690 1700 1710 1720 1730ProbabilityConfidence level Duration (days)BETA CDFBEAT PDF133  3.11.  The results of the benchmark scenario is 883 m/month (10,596 m advanced /year), while the results for the flexible scenario are 1,195 m/month (14,349 m advanced/year).  Development models results revealed that a maximum of 28.0 % and a minimum of 21.9 % of overall development performance improvement are achieved in Blocks 1 and 2, despite the fact that the largest comprehensive model (EFD-6M) showed an improvement of 36% of the development of a drawpoint drift, as shown in Figure 3.23. This is due to the fact that the greater the multitasking of equipment between multiple headings, the greater the resulting performance improvement from better equipment utilization.   Figure 3.23 Comparison between extraction crosscut completion times for one AUPC   036912151821242730330 50 100 150 200 250 300 350Completed develepment cycles Time (Hours)El TenienteExtraction Crosscuts(Truck-Haul system)EL TenienteExtraction Crosscuts(Conveyer system)134  Table 3.10 Comparison between the mean values of the benchmark and flexible models Ore handling system model  Development progress (Mean values) Construction progress (Mean values) Block 1 Truck-haul system (189 days) 6.3 months 28.0 % (improvement 1.8 months) (667 days) 22.2 months 14.0 % (improvement 3.2 months) Conveyor system (136 days) 4.5 months (569 days) 19.0 months Block 2 Truck-haul system (82 days) 2.7 months 21.9 % (improvement 0.6 months) (338 days) 11.2 months 17.7 % (improvement 5.2 months) Conveyor system (64 days) 2.1 months (278 days) 9.2 months Block 3 Truck-haul system (282 days) 9.4 months 26.2 % (improvement 2.5 months) (984 days) 32.8 months 15.8% (improvement 2.5 months) Conveyor system (208 days) 6.9 months (829 days) 27.6 months Total Truck-haul system (553 days) 18.4 months 26.2 % (improvement 4.8 months) (1989 days) 66.3 months 15.7 % (improvement 10.4 months or 0.87 years) Conveyor system (408 days) 13.6 months (1676 days) 55.9 months  Table 3.11 Comparison between the mean values of the development rates for the benchmark and flexible models  Ore handling system Development rate (advanced meter / month) Construction rate (drawbell / month) Block 1  Truck-haul system 880 352 m/month Improvement 2.93 0.49 DB/month Improvement Conveyor system 1232 3.42 Block 2 Truck-haul system 906 259 m/month Improvement 2.59 0.56 DB/month Improvement Conveyor system 1165 3.15 Block 3 Truck-haul system 879 319 m/month Improvement 2.89 0.55 DB/month Improvement Conveyor system 1198 3.44 Total Truck-haul system 883 312 m/month Improvement 2.85 0.53 DB/month Improvement Conveyor system 1195 3.38  In construction models, however, the benchmark and flexible scenarios results are 2.85 DB/month (an average of 34.2 DB/year) and 3.38 DB/month (an average of 40.56 DB/year), respectively, as shown in Table 3.11.  The entire construction phase can be completed in 55.9 months utilizing the conveyor system, compared to 66.3 months using the truck-haul system, which indicates an improvement of approximately 0.53 DB/month.  With respect to the production start-up phase, construction schedule can be reduced by 2.4 months (from 16.4 to 14 135  months) or, in other words, full production phase can start 2.4 months (12 %) earlier than 16.4 months.  Figure 3.20 shows that the worst case situation, where 10-day mucking is expected for one drawbell, which may lead to serious delays and huge reduction in the economic value.  This case showed that the production start-up phase is achieved after 19 months and the entire construction phase is completed in approximately 78 months, as opposed to 66 months, as in the case with the benchmark model.   Despite the fact that the flexible construction model can improve the DB construction rate to achieve 3.38 DB/month, the planned target rate was still under 4 DB/month.  This may lead to postponing the production start-up phase by two months, as the mine expected the commencement of full production after roughly 12 months, since the first drawbell has been blasted. However, this rate is significantly enhanced from the benchmark model, in which the production start-up phase may take up to 16 months, or four months of delay from when the planned construction target is expected.   3.11.4 Flexibility in Extraction Level Results El Teniente and Offset Herringbone were both compared in terms of development performance. It was of interest here to compare the time saved by implementing the El Teniente style while maintaining the awareness that both layouts carried advantages and disadvantages with respect to geotechnical, safety, and construction benefits. It should be stressed that drawpoint spacing and extraction level design were kept identical for a valid comparison of the two layout approaches. Both the truck-haul and conveyor ore handling systems were considered. Simulation results indicated that the development of extraction crosscuts were the schedule-critical paths among the 136  three infrastructure levels in Offset Herringbone models, despite the fact that the requirements of drifting in a smaller progress cycle differs from the larger ones as shown for example in Figure 3.24.  Results for individual CDM and SDM models for both layouts are depicted in Tables 3.12 and 3.13.  Simulation runs are given in Appendix B.    Figure 3.24 Completion times for one progress cycle requirement in the Offset Herringbone development model - one random simulation run for AUPC-1     01234567890 20 40 60 80 100 120 140 160 180 200 220Completed develepment cycles Time (Hours)Offset Herringbone (crosscuts)Offset Herringbone (apex)Offset Herringbone (extraction)Offset Herringbone (undercut)137  Table 3.12 Simulation results:  El Teniente versus Offset Herringbone  Development model El Teniente Style  Truck-haul system (CDM-EH models) Conveyor system (SDM-EV models) Mean µ𝑡  (hours) Variance Standard Deviation 𝜎𝑡 (hours) Mean µ𝑡  (hours) Variance Standard Deviation 𝜎𝑡 (hours) AUPC-1 205.40 121.60 11.03 169.40 153.60 12.39 AUPC-2 209.20 165.51 12.87 177.80 46.40 6.81 AUPC-3 246.30 100.90 10.04 192.30 200.90 14.17 AUPC-4 253.40 89.60 9.47 195.80 38.40 6.20 AUPC-5 321.80 46.40 6.81 217.40 89.60 9.47 Development model Offset Herringbone Style  Truck-haul system (SDM-OH models) Conveyor system (SDM-OV models) Mean µ𝑡  (hours) Variance (hours) Standard Deviation 𝜎𝑡 (hours) Mean µ𝑡  (hours) Variance  Standard Deviation 𝜎𝑡 (hours) AUPC-1 214 204.44 14.30 178 76.10 8.72 AUPC-2 231 33.60 5.80 190 206.40 14.37 AUPC-3 265 57.60 7.59 204 110.04 10.49 AUPC-4 303 248.18 15.75 220 100.44 10.02 AUPC-5 333 87.57 9.36 233 166.77 12.91  Table 3.13 Comparison between the mean values of the comprehensive development models  Development model Development progress Truck-haul system Conveyor system El Teniente (CDM-EH) Offset Herringbone (SDM-OH) Difference El Teniente (SDM-EV) Offset Herringbone (SDM-OV) Difference Mean µ𝑡  (hours) Mean µ𝑡  (hours) (%) Mean µ𝑡  (hours) Mean µ𝑡  (hours) (%) AUPC-1 205 214 - 4.39 % 169 178 -5.32 % AUPC-2 209 231 -10.52 % 178 190 -6.74 % AUPC-3 246 265 -7.72 % 192 204 -6.25 % AUPC-4 253 303 -19.76 % 196 220 -12.2 % AUPC-5 322 333 -3.40 % 217 233 -7.37 %  Both development models utilizing the conveyor system perform better than those employing the truck-haul system. Simulation results with respect to the conveyor system indicated that 408 days (13.6 months) and 443 days (14.7 months) respectively are required to complete the development 138  work within the footprint in the El Teniente and Offset Herringbone, with approximately an 8.58 % reduction in speed in the Offset Herringbone, as shown in Figure 3.25 and Tables 3.14 and 3.15. Likewise, simulation results with respect to the truck-haul system showed a reduction of 9.4 % between both layouts, in which 553 days (18.4 months) and 605 days (20.1 months) respectively were required to complete the development work within the footprint in El Teniente and Offset Herringbone. Thus, the mine may potentially save 1.1 month using the conveyor system and 1.7 months using the truck haul system.   Table 3.14 Simulation results for the Offset Herringbone development models (Scenario-OSH)  Development Model (Truck-haul system) Scope of Develop-ment (meters) Statistical results  Mean µ𝑡  (days) Var. (days2) Stand. Dev. 𝜎𝑡 (days) OPT a (days) PES b (days) Beta   Beta   Block 1 16 AUPCs 5,514 201.8 3.23 1.8 188.5 211.4 22.31 16.10 Block 2 8 AUPCs 2,424 94.8 2.41 1.6 87.9 100.2 7.60 5.95 Block 3 25 AUPCs 8,204 308.4 6.08 2.5 286.3 324.0 31.75 22.41 Total 49 AUPCs 16,142 605.0 11.73 3.4 562.6 635.6 64.61 46.63  Table 3.15 Simulation results for the Offset Herringbone development models (Scenario-OSV) Development Model (Conveyor system) Scope of Develop-ment (meters) Statistical results Mean µ𝑡  (days) Var. (days2) Stand. Dev. 𝜎𝑡 (days) OPT a (days) PES b (days) Beta   Beta   Block 1 16 AUPCs 5,514 146.7 4.17 2.0 135.8 162.9 17.354 25.791 Block 2 8 AUPCs 2,424 70.8 1.61 1.3 65.7 74.8 6.205 4.866 Block 3 25 AUPCs 8,204 226.1 5.58 2.4 209.5 244.8 24.873 28.019 Total  49 AUPCs 16,142 443.5 11.36 3.4 411.0 482.6 49.443 59.484  139   Figure 3.25 Simulation results for the development strategies:  Offset Herringbone versus El Teniente layout   The impact of utilizing a specific ore handling system is similar in both layouts.  In the Offset Herringbone models, the entire development progress has been improved by 26.72 % utilizing the truck-haul system, in which each individual block showed approximately 26 % improvement. Likewise, in the El Teniente models, 26.22 % is the improvement in the development speed by 010002000300040005000600070008000900010000110001200013000140001500016000170000 60 120 180 240 300 360 420 480 540 600Development (meters)Model simulation(days)Truck-Haul system (Offset Heringbone)Conveyer system (Offset Heringbone)Truck-Haul system (El Teniente)Conveyer system (El Teniente)140  utilizing the conveyor system. The Beta CDF and PDF results are shown in Figures 3.26 and 3.27 for these development models.    Figure 3.26 Beta CDF and PDF for extraction level Offset Herringbone model (truck-haul system)    Figure 3.27 Beta CDF and PDF for extraction level Offset Herringbone model (conveyor system) 0%5%10%15%20%25%30%35%40%45%0%10%20%30%40%50%60%70%80%90%100%560 570 580 590 600 610 620 630 640ProbabilityConfidence level Duration (days)BETA CDFBETA PDF0%5%10%15%20%25%30%35%40%0%10%20%30%40%50%60%70%80%90%100%400 410 420 430 440 450 460 470 480 490ProbabilityConfidence level Duration (days)BETA CDFBETA PDF141  A comparison of the development speed is shown in Table 3.16. Most Offset Herringbone models reveal less than 10 % of the difference in development speed, except those models that simulate Block 2. Since this block is the smallest among the other two, the impact was higher than with other blocks by a difference of 15.85 % between both extraction styles. In conclusion, the cost premium to spend on developing an additional of 3% on drawpoint drives in the  El Teniente layout results in an improvement in development speed by an average of 9 %.    Table 3.16 Comparison between the expected development targets Extraction layout  Development progress Truck-haul system Mean µ𝑡 (days) Difference in Mean Values Conveyor system Mean µ𝑡 (days) Difference in Mean Values Block 1  El Teniente 189 -6.87 % 136  -8.08 % Offset Herringbone 202 147  Block 2 El Teniente 82 -15.85 % 64  -9.37 %  Offset Herringbone 95 70 Block 3 El Teniente 282 -9.21 % 208 -8.65 % Offset Herringbone 308 226 Total El Teniente 553 -9.40 % 408 -8.57 % Offset Herringbone 605 443   Offset Herringbone models encounter less overall development requirements than the El Teniente layout, despite the fact that they have more development cycles, four 2.5 m and four 4 m cycles as shown in Table 3.17. It was found that 4,066 and 4,319 cycles were required to develop the El Teniente and Offset Herringbone layouts respectively. However, since 756 of the total number of cycles in Offset Herringbone are 2.5 meter length cycles then 16,264 and 16,142 meters were required to develop the El Teniente and Offset Herringbone layouts respectively. In particular, those differences happen to be in drawpoint and drawbell drives, as shown in Table 3.17. It was expected that only 2.4 % would be the difference between the developments of the extraction drawpoint drives between both types of layout.   142  Table 3.17 Development Cycles and Meters Required for El Teniente and Offset Herringbone Layouts  Infrastructure level Development scope requirements   El Teniente Offset Herringbone Number of Development cycles Cycle length (m) Development meters Number of Development cycles Cycle length (m) Development meters Apex Drives 1001 4 4004 1001 4 4004 Undercut Drives 805 4 3220 805 4 3220 Extraction Drives 1001 4 4004 1001 4 4004 Drawpoint Drives 1259 4 5036 756 4 3024 Drawbell Drives 756 2.5 1890  3.11.5 Flexibility in Undercut Level Results So far the flexibilities in the ore handling system and extraction level indicate significant enhancement in construction speed in spite of the fact that the planned construction target of building 4 DB/month in such narrow ore body has not been achieved. Providentially, however, the results obtained from changing the strategy of undercut sequencing from side-sequencing to middle-sequencing show significant improvements in the speed of construction. Since middle-sequencing can be conducted either from the middle of Block 1 or anywhere inside the ore body, simulation results depend entirely on the number of available open faces in each AUPC, regardless of where the undercut starting point is.   Of interest here are the results for construction performance in terms of the rate of building drawbells since those are the critical paths.  Statistical results for middle-sequencing are presented in Table 18. As expected, the mean values for Case 1 and Case 2 utilizing the conveyor system show quicker advancement than those utilizing the truck-haul system.  The beta PDF and CDF for those flexible models are depicted in Figures 3.28 and 3.29.  143  Approximately 1,298.9 days (43.30 months) and 1,349.1 days (44.97 months) are required, with a 50 % chance to build 189 drawbells for Case 2 and Case 1, respectively, using the conveyor system.  This translates to an average construction rates of 4.37 DB/month and 4.20 DB/month utilizing higher and lower numbers of equipment, as in Case 2 and Case 1.  With regard to the truck-haul system, the entire construction phase is likely to be completed in approximately 1,426.5 days (47.55 months), with an average rate of 3.98 DB/month and 1,493.2 days (49.77 months) with an average rate of 3.80 DB/month for Case 2 and Case 1, respectively. It should be noted that results acquired for the truck-haul system and Case 1 are the only ones that indicated a performance slightly lower than the planned target rate.   Table 3.18 Simulation results for the middle-sequencing construction model (Scenario-EMH verse Scenario-EMV) Construction Model  Scope of Construction (Drawbell) Statistical results Mean µt  (days) Var. (days2) Stand. Dev. σt (days) OPT a (days) PES b (days) Beta   Beta   (Truck-haul) Case 1 189 1493.2 23.80 4.9 1467.0 1529.2 16.13 22.16 Case 2 189 1426.5 13.02 3.6 1415.6 1447.8 5.73 11.19 (Convey-or) Case 1 189 1349.1 6.82 2.6 1326.0 1361.5 26.92 14.45 Case 2 189 1298.9 4.01 2.0 1286.0 1314.6 22.39 27.25   144   Figure 3.28 Beta CDF and PDF for middle-sequencing models:  (truck-haul system)    Figure 3.29 Beta CDF and PDF for middle-sequencing models:  (conveyor system)   0%5%10%15%20%25%0%10%20%30%40%50%60%70%80%90%100%1400 1420 1440 1460 1480 1500 1520 1540ProbabilityConfidancce level Duration (days)BETA CDF (Truck-HaulCase 1)BETA CDF (Truck-HaulCase 2)BEAT PDF (Truck-HaulCase 1)BETA PDF (Truck-HaulCase 2)0%5%10%15%20%25%30%0%10%20%30%40%50%60%70%80%90%100%1280 1300 1320 1340 1360 1380ProbabilityConfidancce level Duration (days)BETA CDF (ConveyorCase 1)BETA CDF (ConveyorCase 2)BEAT PDF (conveyorCase 1)BETA PDF (ConveyorCase 2)145  Results obtained for the flexible models expose significant construction achievement, compared to benchmark models for both ore handling systems, as shown in Table 3.19.  Flexible model results for Case 1 and Case 2, along with benchmark results, are shown in Figures 3.30 and 3.31.  An approximately 18 % increase in construction speed is expected in the truck-haul system with 10-day mucking, compared to 25 % in 5-day mucking models for Case 1.  An approximate improvement of 20 % is expected with the conveyor system for Case 1, as well.  However, the ability to exercise the crashing option in the middle-sequencing, as in Case 2 and increase in the number of machines utilized results in approximately a 30 % increase in construction speed expected in the truck-haul system with 10-day mucking, compared to 28 % in 5-day mucking models for Case 2 and a slightly more than 20 % speed gain is predicted in the conveyor system models.   Table 3.19 Summary and comparison between the mean values of the Construction Progress Rates (Side-Sequencing verse Middle-Sequencing Cases 1 and 2) Ore handling system  Construction  progress Side-sequencing (Benchmark case) Middle-sequencing  (case 1) Middle-sequencing  (case 2) months Rate  DB/ month months Progress Improve-ment % Rate  (DB/ month) months Progress Improve-ment % Rate  DB/ month Truck-haul system (10-day mucking) 78.0 2.42 64.0 17.94 % 2.95 55.0 29.49 % 3.44 Truck-haul system (5-day mucking) 66.3 2.85 49.8 24.89 % 3.80 47.6 28.20 % 3.98 Conveyor system 55.9 3.38 45.0 19.50 % 4.20 43.3 22.54 % 4.36      146   Figure 3.30 Simulation results for the construction strategies:  side-sequencing (Scenario-ESH and Scenario-ESV) versus Middle-sequencing Case 1 (Scenario-EMH and Scenario-EMV)  0204060801001201401601802000 10 20 30 40 50 60 70Construction (drawbells)Model simulation (month) Flexible model Case 1  (Truck-Haul system ,Middle-sequencing)Flexible model Case 1 (Conveyor system ,Middle-sequencing)Benchmark model (Truck-Haul system ,Side-sequencing)Benchmark model (Conveyor system ,Side-sequencing)147   Figure 3.31 Simulation results for the construction strategies:  side-sequencing (Scenario-ESH and Scenario-ESV) versus Middle-sequencing Case 2 (Scenario-EMH and Scenario-EMV)     0204060801001201401601802000 10 20 30 40 50 60 70Construction (drawbells)Model simulation (months)Flexible model Case 2 (Truck-Haul system, Middle-sequencing)Flexible model Case 2 (Conveyor system ,Middle-sequencing)Benchmark model (Truck-Haul system ,Side-sequencing)Benchmark model (Conveyor system ,Side-sequencing)148  3.11.6 Discussion of the Results Simulation models were developed specifically for the development and construction processes of the New Afton mine and evolved conspicuously from typical, comprehensive, and scenario models.  Verification and model validation were carried out to ensure that the data used and model assumptions were adequate, reasonable, and correct to develop the logic that would be used to build the models, then to testing the model for software and modeling errors that could result in misleading the results, and, eventually, to guarantee that those development and construction models were reliable to be employed with confidence within the intended purpose of this study. Because New Afton is a relatively small mine with a relatively high aspect ratio (high length over narrow width) and, thus, can encompass up to a maximum of five drawbells, the results in construction of drawbells being in the critical path. However, in the large block cave, mines where several open faces are available for construction activities, development activities are normally critical to the schedule.   Simulation model results confirm that using the conveyor system early in the construction phase adds significant improvement in the construction speed and development advance rates. Likewise, the results obtained from changing the strategy of undercut sequencing from side-sequencing to middle-sequencing indicate substantial improvements in the speed of construction.   Results for the three flexible scenarios compared to the benchmark model are summarized as follows:  No matter what ore handling system is utilized for mucking, all construction models utilizing side-sequencing exhibit a drawbell construction rate below 4 DB/month, despite 149  the fact that the conveyor system has higher performance by an average of 16 % of construction progress.   Although Offset Herringbone style models involve an average of 2.4 % less development requirements, the development progress is slower than El Teniente style models by an average of 9.4 % and 8.6 % employing the truck-haul and conveyor systems, respectively.   Development models reveal similar improvements by either developing the El Teniente or Offset Herringbone when employing the conveyor system, in which performance improvements are expected at an average rate of 26 %.  Ultimately, it is clearly envisaged that the middle-sequencing option can significantly improve the mine construction rates in both cases where construction crashing can be applied, as in Case 2, since the accessibility of more open faces leads to better equipment utilization.   With the undercut flexible strategy in Case 2, the mine can utilize the truck-haul system and switch to the conveyor system if the mine encounters risks of delays and needs to accelerate construction from 3.98 DB/month (original target) to 4.36 DB/month, which is the maximum the mine can achieve under these conditions of mine design, extraction style, undercut strategy, ore handling system, and equipment.    The next Chapter discusses the third step of planning for flexibility, namely pricing those strategies.  The DES results obtained from the benchmark and scenario models for the development and construction work packages can be used to establish a capital expenditure cash flow. Production cash flow furthermore can be estimated from the construction models in which 150  the progress of building the first 47 drawbells depicts the start-up phase and the full production phase can be estimated from the target production capacity that is correlated with the opening of new active drawbells, allowable draw rate, and expected life of drawbells. A method based on least-square Monte Carlo real options (LSM) to calculate the capital cost inclusive of contingency was developed based on the expected delays in the construction schedule. DES armed with LSM simulation results are integrated to construct a cash flow that could ultimately be used to estimate the expected economic value for such large-scale projects.    151  Chapter 4: Pricing of Flexibility in Cave Mining Construction  4.1 Introduction In this chapter, a real options approach based on the least-squares Monte Carlo method (LSM) is developed to estimate cost contingency associated with schedule uncertainty in construction projects from a contractor’s perspective. Normally, a contractor’s project managers would make timely decisions during the construction execution phase and before the final project completion date to exercise the crash or acceleration option to maintain the planned schedule baseline. Thus, cost contingency is estimated in the construction planning phase to cover the cost of potential endogenous project crashing decisions.   Thus, the contribution of this chapter is to describe a method that is able to respond to schedule uncertainties in construction projects by incorporating the decision-making tactic of project crashing into the budget, including the contingency valuation, using the framework of real options and Monte Carlo simulation from a contractor’s perspective. The LSM is a Monte Carlo simulation method originally developed by Longstaff and Schwartz (2001) for approximating the value and optimal exersise of  financial derivatives that can be exercised anytime prior to and including its maturity dates (American style option). The LSM technique can handle complex options with multiple underlying variables. It is difficult to value American-style options based on traditional Monte Carlo because of the inability to deal with the early exercise dates of American options. Likewise, other real options techniques can only deal with one or at most a few sources of uncertainty.  152  The main contribution herein is the development of an algorithm that can estimate and allocate cost contingency over project work packages in order to pay for not extending the schedule (i.e., to avoid delays). The value of the crashing option was explicitly formalized into the process of valuation, as it is assumed to be a single option being considered in the valuation at every decision point (e.g., decisions normally made at project milestones, yearly, quarterly, or monthly).   As a part of the proposed method, a stochastic function that can be integrated into a framework of numerical simulations was developed. This ensured that this function can implicitly account for sources of schedule uncertainties for projects represented by multiple and overlapping work packages. It should be noted though that technical difficulties, due to, for example, equipment breakdowns, geotechnical problems, or shortages of resources, are not explicitly formulated into the stochastic process. Instead, statistical results for work packages, which can be obtained from previous projects or, in some cases, by means of simulation, can be employed to simulate the actual process of construction and used to establish the stochastic function. For example, DES can model the actual process of construction at the work package or activity level and incorporate the activities durations, network logic and sources of delays pertinent to a particular project. The results yielded by the DES can be displayed in a histogram that depicts work package durations and associated probabilities. Those results serve as inputs to the developed stochastic function in the LSM method.     153  4.2 Literature Review  In large-scale construction projects, for example a high-rise building, an underground cave mining system, or a sports stadium, very significant capital allocation and time commitments are required to arrive at full-scale operation. Risks and uncertainties of such projects are significantly higher than for small-scale projects, due to the complexity and interactions of the project schedule components, and the scale and uniqueness of large-scale projects. One way to successfully manage uncertainties and potential risks that would lead to schedule delays and associated cost overruns is to include a reasonable cost contingency in the budget baseline (Mac & Picken, 2000; Sonmez et al., 2007; Idrus et al., 2010). A contractor’s budget typically includes indirect, direct, and overhead costs, as well as mark-up for risks and profit (Dikmen et al., 2007; Polat & Bingol, 2013) in which cost contingency is added to the cost base estimate to calculate the budget baseline or, simply, the budget.  Contractors face challenges to deliver large-scale projects within the assigned budget and on schedule. A reasonable assumption is that the better is the evaluation of budget inclusive of risk mark-up, the better would be the time and cost performance of the project. Determining the correct budget helps contractors achieve their cost objectives and target profit margin, whereas low or high cost contingencies may result in potential of project failure or the contractor losing the contract, respectively (Tseng et al., 2009; Polat & Bingol, 2013). Thus, an adequate approach to accounting for sources and impacts of project delays and, at the same time, incorporating construction decision-making tactics into the valuation process of estimating cost contingency can be a key element to successful project delivery.   154  Contingency estimation can be highly subjective. Normally, risks are shared between contractors and owners, and are allocated according to the type of the contract (e.g., lump sum, cost plus, unit price, etc.), which explicitly states who is the bearer of the risk (Espinoza 2011). One challenge, however, is the fact that contingency estimation is subject to the risk perceptions of project team members. Another potential issue can arise from the question of what items to include or exclude in contingency allocation. It is also common practice to avoid increasing the allocation of contingency for the purpose of making project proposals economically attractive (Espinoza 2011). As noted by Panthia et al. (2009), cost estimators are the key determinant in contingency estimation in which his/her experience results in the estimation being overly simplistic or rational. Also, there is a substancial role for senior management in setting a contengency allowance.   As described by the Association for the Advancement of Cost Engineering (AACE International), cost contingency is defined as, "an amount added to an estimate to allow for items, conditions, or events for which the state, occurrence, or effect is uncertain and that experience shows will likely result, in aggregate, in additional cost” (AACE, 2007). It can be implied from this definition that contingency covers foreseen events (known unknowns), and unforeseen events (unknown unknowns). Depending on the nature of the contractual agreements between the contractor and the client, contractor cost contingency is usually meant to cover the technical uncertainty (e.g., the technical difficulty) related to the time required to complete the scope of work and market uncertainty (e.g., price fluctuation with time of the unit needed to complete the project) (Espinoza 2011). However, client scope changes or client designer errors, change of site conditions, and external force majeure risk events (e.g., hurricanes, earthquakes, political events or legal decisions) are not meant to be part of contractor cost contingency.  155  Contingency estimation using subjective judgment as a fixed number or percentage addition to the base estimate is often deemed unsatisfactory because it is arbitrary and difficult to justify (Idrus et al., 2010) and has low accuracy (Baccarini, 2004). It is commonly based on initiative judgment, historical data, past experience, and rule of thumb (PMBOK® Guide, 2008). This traditional method typically has been criticized and is believed to be the reason why many projects are completed over budget (Adfin et al., 2014; Bello and Odusami, 2008). Baccarini (2004) investigated the accuracy of cost contingency for 48 road construction projects in Australia. A foremost finding was that the average construction cost contingency was 5.24% of the awarded contract value, whereas the average value of contract variations was 9.92%. It showed a significant shortfall in traditional contingency estimation accuracy due to the current practice of using a deterministic approach.    The subject of contingency estimation has gained a great deal of attention in research during the last decade since contractors are looking for robust approaches for contingency estimation. Various methods of contingency estimation and allocation have been discussed in the literature, including, for example, statistical approaches and probability theory (Yeo, 1990), risk analysis (Mac & Picken, 2000; Panthia et al., 2009), belief network (Kalafalah et al., 2005), probabilistic approach (Touran, 2003a, 2003b), parametric modeling using linear regression (Thal, Jr. et al., 2010), fuzzy logic, and multiple regression (Polat & Bingol, 2013). One limitation affecting these valuation models is the ignorance of the cost of the decisions made by the project managers, who frequently respond to schedule uncertainty and take necessary actions during the project execution phase, in order to ensure successful delivery. However, disregarding the decision-making process in the 156  contingency estimation may potentially lead to greater discrepancy between the estimated and actual costs (Tseng et al., 2009).  Contingency estimation using the real options technique and stochastic dynamic programming was introduced by Tseng et al. (2009). Tseng et al. developed a real options model from a client’s perspective using the single-factor trinomial tree model proposed by Hull and White (1994). Delays due to extrernal risk events and change orders (or design changes) are two uncertainy variables considered and are assumed to follow the Bernoulli distribution and the normal distribution, respectively. All real options available to the client are generalized in a single option by which to expedite or crash the project schedule. One limitation is that this model is not suitable for modeling with several underlying variables. Espinoza (2011) developed a closed-form solution for contingency adjusted project budgets from a contractor’s perspective, similar to Black and Schole (1973), which is commonly used for pricing European-style options that can be only exercised at the option maturity date. Market and technical uncertainties are modeled based on the stochastic process proposed by Pindyk (1993). This model is not suitable for modeling American-style options which can be exercised any time before or at the option maturity date (expiration date).    The ability to exercise construction crashing as an option is critical to proactively adapting to schedule uncertainty that can delay critical activities or work packages. Crashing or accelerating an activity or a work package means a method, tactic, or technique used to compress the duration of this activity and lag time. It involves making schedule and cost trade-offs by determining how much to shorten the duration of a schedule by the least increment of cost (PMBOK® Guide, 2008). 157  There are several ways to crash activities, with the most common being providing additional resources, using overtime and multiple shifts, and changing the construction method and technology.   4.3 LSM Real Options Framework Boyle (1977) used the Monte Carlo method to compute the value of European-style options (e.g., options can only be exercised at the final expiration date).  Longstaff and Schwartz (2001) developed a method to compute the value of an American-style real option based on least-squares Monte Carlo simulations. The least-squares Monte Carlo is a numerical technique that can handle complex options with multiple underlying variables (e.g., unit costs, exchange rate, inflation rates, production rates, etc.).  Although other options techniques can value American-style options (e.g., Bjerksund and Stensland, 1993), they still can only deal with one or, at most, a few sources of uncertainties, with mathematical complexity.   LSM simulation is a computationally efficient path-dependent procedure used for valuing several sources of uncertainties and non-uniform components of cash flow. The basic idea is to simulate multiple realizations of uncertain variables and market conditions using the Monte Carlo technique and make optimal decisions (i.e. change mine production plans with time based on new market conditions) in each time period using value expectations (Dimitrakopoulos and Abdel Sabour, 2007). LSM simulation has been extended to value real capital mineral resource projects (Abdel Sabour and Poulin, 2006). Choosing an optimum mine design among different alternatives, real options using simulations is practically implemented for a gold mine to value the option of abandon 158  by utilizing multiple underlying variables, such as exchange rate, metal price, and geological uncertainties (Dimitrakopoulos and Abdel Sabour, 2007).   The strengths and limitations of the Monte Carlo method have been discussed in extant literature (Boyle, 1977). Boyle, for example, discussed the advantages obtained when the underlying asset returns are generated by different stochastic processes. In particular, the author highlighted the value of using the distribution formed by the parameter data set, rather than single-point estimates pertaining to the problem under investigation. Distributions used in the Monte Carlo method do not require closed-form analytical expression to estimate the asset returns. One drawback of the Monte Carlo method is the fact that the standard error of the estimate is inversely proportionate to the square root of the number of simulations. Thus, a large number of simulations is required to obtain a small confidence interval for an estimate.  4.4 LSM Method in Construction 4.4.1 LSM Method Overview and Assumptions  In any construction project, work package durations are estimated based on the scope of the work required to complete the entire project and the resources utilized. These durations enables the construction schedule to be determined, utilizing the logic of the schedule network that connects those work packages together. In this process, it is essential to accommodate the varying unit costs, as these are usually work package-specific, and are estimated based on the unique resources (e.g., cost of the material, equipment, manpower, etc.) used in any work package. Similarly, scope and time parameters can be used to determine the planned progress rate (work rate) for a work package. In the proposed LSM method, progress rate for any work package is 159  assumed to be constant, even though, in practice, it is a function of the productivity of resources employed in any particular work package.  The stochastic function used in the proposed LSM required developing an expression for the percentage of remaining scope of work for the remaining duration of the entire project. The planned work rates for work packages and their respective unit costs, along with random variables represented by a probability density function to account for delays, were integrated to derive this stochastic function. In addition, to allow contingency to be estimated, a project cost function was derived using these scope, time and cost parameters, as well as a variable representing the amount of effort required for crashing.   The effort level variable that accounts for the extent of crashing was also introduced, as a means of maintaining the schedule. The amount of crashing represented by this variable has to be optimized based on the realized level of delays at any given time during the project execution. Thus, the proposed method involved estimating the optimized project cost function using least-squares analysis technique. Although the optimized cost function incorporates the optimized effort level for crashing, construction crashing decisions are subjected to conditions of delays. Thus, LSM incorporated the decision-making process into the valuation in which the estimated optimal level of project crashing is chosen only if delays are encountered.  One main assumption underlying this approach is that the work packages are not connected by a formal schedule network logic. A detailed determination of activity-based schedule network in each work package is not considered herein and is assumed to be already conducted in estimation 160  of the start date and duration of each work package. Each work package is assumed to have a fixed start date, and is completed by the end of the interval. In addition, the work related to individual work packages can only be extended. The entire planned project schedule is divided into constant time intervals (for example, a suitable time interval would be one month for a three-year-long project). It is also assumed that the random variable representing delays used in the stochastic function is independent of time, and is only affected by work package characteristics.   Another noteworthy assumption is that project crashing is a single option being considered in the valuation. In other words, if delays are encountered during any time period (interval) and crashing is exercised in the subsequent time step, all work packages in the subsequent time interval are crashed at this particular time interval at the same estimated effort level. Finally, it is assumed that cost contingency covers only the cost required for crashing, even though the increase in unit costs due to inflation, exchange rates, etc., should also be incorporated in practice.     4.4.2 Proposed LSM Method  In the construction planning phase, the proposed LSM method involves four distinct steps. The first step consists of developing a stochastic process that estimates the scope of work, accounting for the individual level of delays in each work package at every time. The second step involves identifying the conditional expected cost function in order to calculate the incurred budget at every time interval (time period).  The third step involves estimating the optimized amount of incurred budget by solving the condition expected function using least-squares regression analysis. The last 161  step explicitly engages the decision-making process into the valuation in which the optimal level of project crashing is chosen based on the encountered delay as project crashing is assumed to be a single option being considered in the valuation.  1) Simulation of Underlying Remaining Scope of Work  The first step consists of simulating a sufficient number of realizations (paths) of the evolution of the “aggregated remaining work,” in which the total number of realizations adequately captures the probability distribution of the expected delays. A path refers to one simulation scenario of how the project unfolds. The expression “aggregated remaining work” refers to the percentage of remaining scope of work for the remaining duration of the entire project at any given time.  The term “remaining work”, however,  is defined as the percentage of the scope of work needed to complete only one work package at any given time and can be calculated from the percentage of completion (e.g., either planned or simulated actual) for any work package at that time.   Typically a construction project contains many overlapping work packages and each work package consists of various activities. Thus, the aggregated remaining work at any given time is the summation of the remaining work in each work package remaining to complete the project. In the diagrams shown in Figures 4.1 and 4.2, at 0t  , the aggregated remaining work ( )W t  is equal to 1 (100 %) and at t T , the final completion date, it equals 0. At time t , the planned and forecasted actual aggregated remaining work can be expressed as ( )pW t  and ( )aW t respectively, represented by the planned and actual percentage complete  ( )p t  and ( )a t . The relationship between these variables can be described as:  162   11( ) ( )( ) ( )p pa aW t tW t t     (8)  Figure 4.1 Schematic diagrams of project percentage complete    Figure 4.2 Schematic diagrams of project percentage remaining (aggregated remaining work)  The progress rate function refers to the project rate of work (i.e., project production rate function), measured as a percentage of project complete divided by time (%/time), can be expressed 163  mathematically for either planned progress rate ( )pu t  or forecasted actual progress rate ( )au t  schedules as:  ( ) ( )( )( ) ( )( )p ppa aad t dW tu tdt dtd t dW tu tdt dt                            (9)  In order to derive an expression for the aggregated remaining work and to be able to treat overlapping work packages, an expression for ( )W t  articulated from the scope of work, durations, and unit costs of work packages was sought based on earned value analysis (Anbari, 2003). The first step is to generate an adequate “number of paths” H  (e.g., H  = 5000). A path is one scenario or realization of the aggregated remaining work function. At every time step, the values for the aggregated remaining work are different between a path and another. For every path, however, the simulation of ( )W t  starts from the beginning of the project where 1( )W t  and estimates ( )W t  at every time step until the completion date where 0( )W t . Therefore, the expression of ( )W t  can be developed based on earned values that measures project progress.   The earned value analysis (cost unit, e.g., $) is a measure of progress performance and has the ability to combine project scope of work completed and incurred cost at every time period. Define the difference in the cumulative project planned (forecasted) values from any time jt  to time 1jt  (i.e., the planned progress of work in time interval i ) be denoted by 1i j jPV PV PV  , where jPV  is the budgeted planned value for planned schedule at time jt  as shown in Figure 4.3.  164    Figure 4.3 Schematic diagrams of project earned value analysis  Similarly, the actual work complete at time jt  can be described as jEV  (the earned value). The difference in the earned values between two times 1i j jEV EV EV    indicates the actual work complete at time interval i . PV  and EV  can now be represented in any time interval for planned (original) and forecasted actual schedules in discrete form, as follows:       , 1 , ,i p j p j p iPV W W C W C  (10)   1, , ,i a j a j a iEV W W C W C     (11) where ,p jW  is the planned aggregated remaining work at time t , ,a jW  is the forecasted aggregated remaining work for one simulated path at time jt  and C is the project cost base estimate and does not include cost contingency. Figures 4.4 and 4.5 illustrate project progress in an earned value plot and aggregated remaining plot, respectively, where AC  is forecasted actual costs.  165    Figure 4.4 Schematic diagrams of earned value    Figure 4.5 Schematic diagrams of aggregated remaining work   Considering that a construction project contains many overlapping work packages, each work packages have planned start dates and finish dates in a project schedule baseline. To model projects with multiple work packages, it is assumed that each work package m has a unique progress rate 166  function mq  which is a function of the work productivity mP  that can be achieved by one construction crew for specific work and number of crewsmE .  Also, each individual work rate mq  can be calculated from the scope mQ  and the estimated duration mD  for each work package.    mm m m mQq P E D   (12) In reality, work packages have different scopes of work, resource usage, and productivity of resources, and work package durations can be estimated using those parameters (Hendrickson et al. 1987). For example, in tunnel excavation, mq  can be measured as the meters of advanced in a day, or in a high-rise construction project, the number of constructed of floors per month. It is assumed that the durations, start dates, scope of work, and cost unit (cost per unit of work) of the work packages are known.  For a project with a single work package (e.g. the structure of a high rise building), the difference between the planned values PV  (e.g. $) in any time interval can be defined as follows:   1i i j j iPV q t t c    (13) where iq  (work per unit time) is the progress rate function, and ic  is a unit cost (cost per unit of work) in any time interval.  As shown in Equation 13, the embedded assumption is that there is only one work package in progress. With Equations 10 and 13, an expression for planned values PV  based on iq  and ic  can be extended to capture the multiple work packages in every time interval as follows:  167   11, , , , ,( )mi i n j n j n i n p inPV q t t c W C       (14) The goal is to simulate a sufficient number of paths to represent all possible scenarios of project schedule. To account for forecast earned values EV , the evolution of aggregated remaining work for each path s 1 ( )s H  can now similarly be expressed from the individual parameters of iq  and ic  for each work package and a random variable i  having a beta distribution representing schedule uncertainty as follows:  11, , , , , ,( )mi i n i n j n j n i n a inEV q t t c W C        (15) Using Equations 11 and 15, an explicit expression of aggregated remaining work in which each work package contains a different scope of work, activity duration, unit cost, and level of delay may be derived. The effort level jf  is defined as the level or degree of project acceleration (crashing) to be exercised by the decision maker at time j . The normal value of jf  is 1, indicating no crashing.  If 1jf , that indicates project crashing is imposed at time j .  111, , , , , , , , , , ,, ,( )ms j s i n s i n s j n s j n s i nns j s jf q t t cW WC    (16) The random variable n  is assumed to characterize potential uncertainty and possible delays in every work package. Each work package can have its associated level of delays depending on the estimated productivity parameter nq . The production rate for any work package is represented by 168  the termn nq  .The beta distribution is appealing for many reasons. It is bounded so events can take place only within intervals defined by minimum and maximum values. A beta distribution can also be easily derived using the program evaluation and review (PERT) approximation (Cottrell, 1999). One key assumption in this model is that work packages have fixed start dates and only durations may increase.  Given a lower (optimistic) estimate a, an upper bound (pessimistic) estimate b , and a subjective estimate of the mode (most likely) d , the PERT approximation (Cottrell, 1999) is used to compute estimates of the mean and standard deviation of a corresponding beta distribution of delays with shape parameters   and  . The mean and standard deviation of the delays X are then calculated as follows:   ( ) ( )E X a b a     (17)  22 1( ) ( )( ) ( )Var X b a        (18)  In Equation 16 (the stochastic function), it is assumed that the beta distribution is defined on the interval  0 1,  which defines the lower and upper bound of the distribution as 0a    and 1b  . To obtain the value d  for each work package, the relative difference between the actual pessimistic duration B and the actual most likely duration D is used, as   d B D D  . For example, if the most likely duration of an excavation work package in a high-rise building project is estimated to 169  be six months and could be completed in seven months at most, then the relative difference would be 0.166.  The normalized delays are therefore [0, 0.83, 1].  Using the PERT approximation this gives  = 180,  = 70, E(X) = 0.72, (X) = 0.028 2) Identifying the Conditional Expectation Function of the Budget After simulating the aggregated remaining work for a sufficient number of paths, the second step is to identify the conditional expectation function ( )E k W  where k  is the optimized project cost function in which incorporates the crash option to expedite the project.  As a construction acceleration tactic, crashing is viewed here as an American-style option (i.e., it is a single option that can be exercised at any time step or decision point).   At the outset, define sC  as the calculated “incurred project baseline cost” for every path at every time interval that can be derived, as follows:  11, , , , , , , , , ,( )ms i s j s i n s i n s j n s j nnC f q c t t    (19) where sf  is the original effort level required to complete the scope of work remaining for every path (i.e., for planned schedule), 1sf   indicates no crashing is imposed at time step or decision point j . Define sk  as the calculated “incurred project budget” inclusive of contingency for each path incurred in time interval i :   11, , , , , , , , , , , ,( )mcals i s j s i n s i n s i n s j n s j nnk f q c t t     (20) 170  where calsf  is the calculated effort level decision required to complete the scope of work remaining, and depending on the aggregated remaining work for every path, calsf  may or may not include a means of crashing. Theoretically, it is assumed that the project manager is able to make the effort level decisions at every time step before the start of the next time interval.  The value of the effort level sf  in the cost base estimate, Equation 19, should reflect no additional means for crashing.  However, in the budget inclusive of contingency (Equation 20), the incurred cost at this interval is function of calculated effort level calsf  required if crashing the project at this stage for each path is needed to bring the schedule back on track. Since the original value for the effort level ,s jf is 1 and the aggregated remaining work ranges between 0 and 1,  the values for the calculated effort level calsf  for each path is assumed to be proportionally linear to the difference between the simulated aggregated remaining work sW  and the original (planned) aggregated remaining work pW  as follows:  , , , ,cals j s j s j p jf f W W      (21) In every time step before the beginning of the subsequent time interval, the simulated aggregated remaining work sW  for each path is compared to the planned aggregated remaining work pW , and the decision to implement crashing might be undertaken if the simulated value is higher than the planned (forecasted) value at this time step.  As shown in Figure 4.6, ,x jW  is greater than ,p jW , thus this path required additional effort to expedite the work packages in the subsequent time interval. For example, if 0 7, .x jW   and 0 6, .p jW  , then 1 10, .calx jf  . Theoretically, this can be translated, as the contractor project manager can choose to increase project productivity by 171  approximately 10 % (e.g., increasing resources or overtime) to cope with the encountered delay assuming that this path (scenario) is how the project schedule unfolds at this particular time.   Figure 4.6 Aggregated remaining work and progress rates for three sample paths and planned path  However, the calculated effort level is not the “optimal effort level,” because all realizations (paths) of  ,s jW  are independent of each other, but also, for the same path, dependent on the simulated work package work rate nq . If for an example, H = 5000 independent paths are simulated to account for all possible schedule scenarios, there would be 5000 different values for  ,s jW  at every time step (decision point), thus 5000 independent values for ,cals jf  at this time step.   The goal is to find the optimal value for the effort level ,s jf  which accounts for the optimum amount for the crashing option for each path at each time step taking into account the interdependency between all value ,s jW  in any given time step and the values of ,s iq  at the 172  subsequent time interval, in which ,s jW  and ,s iq  for each path are independent of each other. To achieve this objective, the conditional expectation function is used in the decision-making policy as:      min , calj j jE k W k W f  (22) 3) Solving the Conditional Expectation Function After calculating the incurred budget sk  for every path starting from the beginning of the project, for every time interval, until the final completion date, the third step is to solve the conditional expected function shown in Equation 22. The solution is found by simple regression of the calculated incurred budget sk  in any given time interval i   against the aggregated remaining work ,s jW  at previous time step j . Regression analysis must be undertaken for every time step as shown for example in Figure 4.7.    Figure 4.7 An example of a conditional expectation function at given time interval (plot for 1 time step)  173  The values of the regressed project cost ,s jk constitute the unbiased expected values of the effort level ,s jf  because it takes into account the entire domain of the aggregated remaining work at any given time step and estimate the associated effort level required for crashing based on the realizations of the subsequent work rates. ,s jf  can be recalculated from ,s jk  for every path in every time interval as follows:  11,,, , , , , , , , , ,( )s is j ms i n s i n s i n s j n s j nnkfq c t t  (23) The regressed ,s jf  takes into account the path-dependent values of aggregated remaining work at each time step and the values of progress rates in the subsequent time interval.  For example, as shown in Figure 4.6, if the realized  ,y jW  is higher than ,z jW , then ,caly jf  is calculated to be greater than ,calz jf  and higher than 1 for both paths y and z . However, the value for the subsequent progress rate ,y iq  is greater than ,z iq , thus, the calculated effort level value for ,y jW  have to be reduced, otherwise, over crashing is imposed. The effort level decision variable should account for the simulated subsequent progress rate ,s iq  and ,cals jf  should be a function of the progress rate, as well as a function of the aggregated remaining work.   Alternatively, if another path z  has lower value of ,calz jf  compared to ,calx jf  but the subsequent progress rate ,z iq  is higher than ,x iq  , then ,calx jf  should be adjusted to account for that higher work rate based on the entire spectrum of work rates realised for all paths at this time interval. In some 174  cases for example, two paths have similar aggregated work rates at any given time step, but have two different subsequent progress rates, thus, despite the calculated effort level that will be the same, the regressed value of effort level should account for the subsequent time interval’s progress rates.  Therefore, the regressed effort level is used for determining the optimized budget, inclusive of contingency, estimation instead the calculated effort level. The values of regressed budget and effort level consider the path-dependent probabilities and associated values of work rates.  All paths eventually give good predictions for the overall expected effort level function with regard to the entire probability of delays spectrum.   The conditional expected function is obtained using linear approximation by regressing the realized project costs ,s jk  on the underlying state variable of aggregated remaining work ,s jW  as follows:   , , , ,Ts j s j s j s jy z A    (24) where ,s jy is the “regress” vector (dependent parameters), , Ts jz denotes the transpose of the “regressor” vector (independent parameters) ,s jz , ,s jA is the “coefficient” vector (unknown parameters), and  ,s j  is the error vector. Higher order functions can be other types of polynomials, see (Longstaff and Schwartz, 2001).    This process requires a backward induction calculation in which the regression process starts from the project completion date and proceeds backward at every time step after calculating the incurred budget sk  for every path at every time interval, as discussed in step 2. Define ,s jR  as the 175  “remaining budget” for each path at time step.  Starting from the project completion date, the remaining budget ,s jR  is zero for all paths since the project has completed and all costs have been spent.   4) Choosing the Conditional Decision for Crashing The last step is to decide on whether to take action for crashing or not. This process is applied recursively starting with the project completion date and proceeding backward in time. This mechanism is applied at each decision point (time step). In LSM, for every time step starting from the final completion date, solving the expected conditional function discussed in step 3 must be undertaken prior to deciding on the effort level value required for crashing for that time step.  Steps 3 and 4 have to be undertaken consecutively for a given time step before proceeding to the previous time step. In other words, after regression is completed for time step j , the decision for the effort level for that time step is chosen as:   , , ,,, , ,::s j s j p js js j s j p jf if W Wf f if W W     (25) i.e., one exercises the crash option for those paths which experienced delays or, ,s j p jW W . Otherwise, if , ,s j p jW W , one continues with the original schedule level.   Starting from the project completion date, the total remaining budget ,s jR  can be calculated from the incurred budget ,s jk  using the optimized effort level values ,s jf additional to any remaining 176  budget 1,s jR  from subsequent time intervals conditional on not exercising the crashing option prior to this time. The total remaining budget is expressed as:  1 11, , , , , , , , , , , , ,( )ms j s j s i n s i n s i n s j n s j n s jnR f q c t t R       (26)  In every time interval, the algorithm proceeds recursively to the preceding time step and repeats those stages. Eventually, at 0j  , the final remaining budget is the total budget required for every path.  To calculate the expected budget ( )E R  for the project, all values for the budget for all paths examined should be averaged.  Statistical analysis can also be conducted on the estimated budget histogram (e.g., calculating the statistical moments of the budget).  The contractor may choose the cost contingency fund based on the level of risk perception (e.g., a risk-averse contractor may choose a higher confidence level and calculate the contingency and other funds from the assigned probability density function).  4.4.3 Least-Squares Monte Carlo Algorithm Summarized here is a more detailed 12 step-by-step for applying the 4 step LSM approach elaborated upon in section 4.4.2. 1. Generate number of possible paths H  ( 1 2, ,...S H ) of the aggregated remaining work 1,s jW  using Equation 16. 2. Compute the incurred project baseline cost ,s iC  using Equation 19. 3. Compute the calculated effort level ,cals jf  using Equation 21.  177  4. Compute the incurred project budget ,s ik  using Equation 20.  5. Identify the conditional expectation function   jE k W  using Equation 22.  6. Solve the conditional expectation function that estimates the optimized incurred budget ,s jk  employing linear regression using Equation 24.  7. Recalculate the optimized effort level ,s jf  using Equation 23.  8. Choose the optimum decision of the effort level for crashing ,s jf  using Equation 25. 9. Compute the remaining budget ,s jR  using Equation 26. 10. Proceed recursively to the preceding stage and repeat steps 6, 7, 9, and 4.10. 11. Establish a histogram for all realizations of sR at project start date. 12. Calculate the expected budget inclusive of contingency ( )E R  and the variance ( )Var R  and other statistical moments for the entire project.   4.5 Numerical Example: Project Comprising Two Work Packages  This numerical example is a simplification of the New Afton benchmark model discussed in Chapter 3. It is used to illustrate how the expected budget can be estimated using the LSM method based on only two overlapping work packages.  4.5.1 Model Input Parameters For simplicity, development and construction work packages are expected to be carried out in parallel in the first 18 months, after which the execution of the construction work package continues until the middle of the sixth year, as shown in Figure 4.8. This schedule is determined 178  by the assumption that the planned development and construction schedule baseline is 5.5 years (66 months). In the LSM model, however, the project schedule is assumed to be extended up to maximum of 6.6 years (78 months) to allow for simulating the actual schedule scenarios (paths), as discussed in the LSM step 1. Work package durations are rounded to the nearest month, as one time interval is set to one month. Using the total scope of works and durations for the two work packages, planned work rates were calculated as shown in Table 4.1. Work packages were assumed to have fixed start date, and only their durations can be extended. The estimated unit cost for each work package is shown in Table 4.1. Budgeted planned values, exclusive of contingency, for those two packages were determined based on the scope of work and unit cost, which were calculated as $76.28 million and $23.35 million for development and construction, respectively. Thus, the planned (passive) construction cost is $99,630,000 Canadian dollars, exclusive of any contingency allowance.  First year Second year Third year Fourth year Fifth year Sixth year WP.1 (𝑞1, 𝑐1)                            WP.2 (𝑞2, 𝑐2)    Figure 4.8 Planned schedule for development and construction work packages  Table 4.1 Data input for a project comprising two work packages ID Name Scope of work 𝑄  Unit Work rate  𝑞   = 𝑄/𝑇 Start date   𝑥    months Duration  𝑇    months Unit cost   𝑐      $/work Cost  𝐶 Million $ Cost ratio (%) WP.1 Development 16264 (m) 904 0 18 4,690 76.278 76 WP.2 Construction 189 (DB) 2.86 0 66 123,550 23.351 24  Excusable delays were modeled as a random variable following a beta distribution function, as shown in Table 4.2. Even though each work package would typically be affected by different levels of delay, for illustration purposes, in the example herein, it was assumed that the delay levels used 179  in the LSM model are similar for both work packages and are set at 6%. This estimate is based on the pessimistic value, and the most likely values obtained from the DES benchmark models. In this case, schedule disruption (delays) is characterized as a beta distribution function ( ; , )betaf x  , where 3 915 1 034( ; . , . )betaf x  is equivalent to a triangular distribution 0 0 94 1( ; , . , )f x .   Table 4.2 Data input regarding level of delays (beta distribution parameters) for a project comprising of two work packages  ID Name OPT. a MO.L. M PES. b Mean µ𝑡  Var. Beta (p) Beta (q) WP.1 Development 0 0.94 1 0.791 0.167 3.92 1.03 WP.2 Construction 0 0.90 1 0.791 0.167 4.17 1.27  4.5.2 Model Results  As the first step in the LSM algorithm, planned and simulated aggregated remaining work versus time are depicted in Figure 4.9 for 3 of the 10,000 paths simulated. The subsequent steps in the LSM algorithm have been executed for the simulated 10,000 paths. The expected total budget inclusive of contingency ( )E R  was estimated as $102.64 million versus the base budget of $99.63 million by averaging all values of the final remaining budget. A histogram of the budget is depicted in Figure 4.10. In this case, cost contingency was estimated at $3.011 million (3.02%) additional to the base cost. For different contractor confidence levels, a beta distribution fitted to the histogram can be used to obtain the different values of contingencies as 3 17 8 98( ; . , . )betaf x , as shown in Figure 4.11. Using the beta distribution function obtained for the budget, contingency reserve can be estimated for five different contractor confidence levels, as presented in Table 4.3. For example, at 50%, 70%, and 90% confidence levels, the budget inclusive of contingency was estimated at $10.3.73, $105.06, and $107.16 million, respectively. 180  Table 4.3 Results for the total budget, inclusive of contingency, for two work packages Schedule disruption Beta  (𝛼, 𝛽)    from         Tri (a,m,b) Budget Analysis & Statistics Beta shape parameters (fitted values) Total Budget including Contingency                                                 ($Millions) BETA 𝛼 BETA 𝛽 Minimum Budget ($Millions) Maximum Budget ($Millions) Confidence level 50% Confidence level 60% Confidence level 70% Confidence level 80% Confidence level 90% level of delay Beta     (3.92, 1.03) 3.17 8.98 $99.63 $118.10 Budget $103.73 Contingency $4.10 (4.12%) Budget $104.35 Contingency $4.72 (4.74%) Budget $105.06 Contingency $5.43 (5.45%) Budget $105.92 Contingency $6.29 (6.31%) Budget $107.16 Contingency $7.53 (7.56%)   Figure 4.9 Planned versus simulated evolution for three paths in the numerical example out of 10,000 sample trails (paths)  181   Figure 4.10 Histogram of the budget, inclusive of contingency, for two work packages  Figure 4.11 Beta distribution of the budget, inclusive of contingency, for two work packages   182  4.6 Flexible Scenarios: Project Comprising Seven Work Packages In this phase of the study, four LSM models were developed for the four specific construction and development scenarios used to estimate the construction progress of the New Afton benchmark and scenario models discussed in Chapter 3. The four models employed herein are as follows:  Scenario-ESH: side sequencing, El Teniente layout, and truck-haul system;  Scenario-ESV: side sequencing, El Teniente layout, and conveyor system;  Scenario-OSV: side sequencing, Offset Herringbone layout, and conveyor system; and  Scenario-ELV (Case 2): Middle sequencing, El Teniente layout, conveyor system, optimized equipment level.  4.6.1 Model Input Parameters  The results yielded by the DES models were used as input to the LSM models. Beta distribution functions were estimated using the DES results, as shown in Table 4.4. Each scenario consists of seven major work packages, as depicted in Figure 4.12 − 4.15, while work, time and cost input parameters are presented in Tables 4.5 to 4.8. Base case planned budgeted values, exclusive of contingency, were calculated for those scenarios as $100.32 million for ESH, ESV, and ELV scenarios, and $99.64 million for the OSV scenario, since the Offset Herringbone layout scenario has fewer development requirements compared to the other three El Teniente layout scenarios.     183  Table 4.4 Summary of discrete event simulation results and estimated beta distribution  Scenario Name OPT. a Most L. M PES. b Mean µ𝒕  Var.  Beta (p) Beta (q) Scenario -ESH Development 0 0.94 1 0.79 0.167 3.92 1.03 Construction 0 0.90 1 0.82 0.167 3.55 0.79 Scenario-ESV Development 0 0.95 1 0.80 0.167 3.84 0.98 Construction 0 0.98 1 0.82 0.167 3.58 0.80 Scenario-OSH Development 0 0.95 1 0.80 0.167 3.81 0.95 Construction 0 0.98 1 0.82 0.167 3.55 0.79 Scenario-OSV Development 0 0.91 1 0.77 0.167 4.09 1.19 Construction 0 0.98 1 0.82 0.167 3.58 0.80 Scenario-ELH (Case1) Development 0 0.94 1 0.79 0.167 3.92 1.03 Construction 0 0.98 1 0.82 0.167 3.58 0.80 Scenario-ELH (Case2) Development 0 0.94 1 0.79 0.167 3.92 1.03 Construction 0 0.99 1 0.82 0.167 3.49 0.75 Scenario-ELV (Case1) Development 0 0.95 1 0.80 0.167 3.84 0.98 Construction 0 0.99 1 0.83 0.167 3.43 0.72 Scenario-ELV (Case2) Development 0 0.95 1 0.80 0.167 3.84 0.98 Construction 0 0.99 1 0.83 0.167 3.46 0.73  First year Second year Third year Fourth year Fifth year Sixth year WP.1 (𝑞1, 𝑐1)                            WP.2 (𝑞2, 𝑐2)                            WP.3 (𝑞3 , 𝑐3)                              WP.4 (𝑞4, 𝑐4)                            WP.5 (𝑞5, 𝑐5)                           WP.6 (𝑞6, 𝑐6)        WP.7 (𝑞7, 𝑐7)     Figure 4.12 Work package parameter assignment matrix – Scenario-ESH   First year Second year Third year Fourth year Fifth year Sixth year WP.1 (𝑞1, 𝑐1)                              WP.2 (𝑞2, 𝑐2)                              WP.3 (𝑞3 , 𝑐3)                                WP.4 (𝑞4, 𝑐4)                              WP.5 (𝑞5, 𝑐5)                             WP.6 (𝑞6, 𝑐6)          WP.7 (𝑞7, 𝑐7)       Figure 4.13 Work package parameter assignment matrix – Scenario-ESV   184  First year Second year Third year Fourth year Fifth year Sixth year WP.1 (𝑞1, 𝑐1)                             WP.2 (𝑞2, 𝑐2)                             WP.3 (𝑞3 , 𝑐3)                               WP.4 (𝑞4, 𝑐4)                             WP.5 (𝑞5, 𝑐5)                            WP.6 (𝑞6, 𝑐6)          WP.7 (𝑞7, 𝑐7)       Figure 4.14 Work package parameter assignment matrix – Scenario-OSV  First year Second year Third year Fourth year Fifth year Sixth year WP.1 (𝑞1, 𝑐1)                             WP.2 (𝑞2, 𝑐2)                             WP.3 (𝑞3 , 𝑐3)                               WP.4 (𝑞4, 𝑐4)                             WP.5 (𝑞5, 𝑐5)                            WP.6 (𝑞6, 𝑐6)                WP.7 (𝑞7, 𝑐7)             Figure 4.15 Work package parameter assignment matrix – Scenario-ELV (Case 2)  Table 4.5 Work, time and cost input parameters – Scenario-ESH  ID Work Package Description Work Model Time Model Cost Model Scope of work 𝑄  Unit Work rate  𝑞   = 𝑄/𝑇 Start date   𝑥  months Duration  𝑇  months Unit cost  𝑐    $/work Cost  𝐶 Million $ Cost ratio (%) WP.1 Apex Drive (Development) 4004 (m) 222 0 18 4,200 16.82 16.76 WP.2 Undercut Drive (Development) 3220 (m) 179 0 18 4,200 13.52 13.48 WP.3 Extraction Drive (Development) 4004 (m) 222 0 18 4,600 18.42 18.36 WP.4 Drawpoint Drift (Development) 3024 (m) 168 3 18 5,600 16.93 16.88 WP.5 Crosscut Drift (Development) 2012 (m) 112 3 18 5,600 11.27 11.23 WP.6 Undercut Strips (Construction) 378 (unit) 5.73 2 66 1,6800 6.35 6.33 WP.7 Drawbells (Construction) 189 (unit) 2.86 4 66 90,000 17.01 16.96      185  Table 4.6 Work, time and cost input parameters – Scenario-ESV  ID Work Package Description Work Model Time Model Cost Model Scope of work 𝑄  Unit Work rate  𝑞   = 𝑄/𝑇 Start date   𝑥  months Duration  𝑇  months Unit cost  𝑐    $/work Cost  𝐶 Million $ Cost ratio (%) WP.1 Apex Drive (Development) 4004 (m) 286 0 14 4,200 16.82 16.76 WP.2 Undercut Drive (Development) 3220 (m) 230 0 14 4,200 13.52 13.48 WP.3 Extraction Drive (Development) 4004 (m) 286 0 14 4,600 18.42 18.36 WP.4 Drawpoint Drift (Development) 3024 (m) 216 3 14 5,600 16.93 16.88 WP.5 Crosscut Drift (Development) 2012 (m) 144 3 14 5,600 11.27 11.23 WP.6 Undercut Strips (Construction) 378 (unit) 6.75 2 56 16,800 6.35 6.33 WP.7 Drawbells (Construction) 189 (unit) 3.38 4 56 90,000 17.01 16.96  Table 4.7 Work, time and cost input parameters – Scenario-OSV  ID Work Package Description Work Model Time Model Cost Model Scope of work 𝑄  Unit Work rate  𝑞   = 𝑄/𝑇 Start date   𝑥  months Duration  𝑇  months Unit cost  𝑐    $/work Cost  𝐶 Million $ Cost ratio (%) WP.1 Apex Drive (Development) 4004 (m) 267 0 15 4,200 16.82 16.88 WP.2 Undercut Drive (Development) 3220 (m) 215 0 15 4,200 13.52 13.57 WP.3 Extraction Drive (Development) 4004 (m) 267 0 15 4,600 18.42 18.49 WP.4 Drawpoint Drift (Development) 3024 (m) 202 3 15 5,600 16.93 17.00 WP.5 Crosscut Drift (Development) 1890 (m) 126 3 15 5,600 10.58 10.62 WP.6 Undercut Strips (Construction) 378 (unit) 6.75 2 56 16,800 6.35 6.37 WP.7 Drawbells (Construction) 189 (unit) 3.38 4 56 90,000 17.01 17.07       186  Table 4.8 Work, time and cost input parameters – Scenario-ELV  ID Work Package Description Work Model Time Model Cost Model Scope of work 𝑄  Unit Work rate  𝑞   = 𝑄/𝑇 Start date   𝑥  months Duration  𝑇  months Unit cost  𝑐    $/work Cost  𝐶 Million $ Cost ratio (%) WP.1 Apex Drive (Development) 4004 (m) 286 0 14 4,200 16.82 16.76 WP.2 Undercut Drive (Development) 3220 (m) 230 0 14 4,200 13.52 13.48 WP.3 Extraction Drive (Development) 4004 (m) 286 0 14 4,600 18.42 18.36 WP.4 Drawpoint Drift (Development) 3024 (m) 216 3 14 5,600 16.93 16.88 WP.5 Crosscut Drift (Development) 2012 (m) 144 3 14 5,600 11.27 11.23 WP.6 Undercut Strips (Construction) 378 (unit) 8.80 2 43 16,800 6.35 6.33 WP.7 Drawbells (Construction) 189 (unit) 4.40 4 43 90,000 17.01 16.96  4.6.2 Model Convergence (Choosing H) Simple trade-off analysis between computational time and number of simulated paths was conducted to decide on the minimum number of favorable paths needed to achieve the required model accuracy. Eight different trials were chosen for this purpose, ranging from 10 to 10,000 paths, which were plotted in a log-scale plot with respect to the forecasted budget and computational time. As shown in Figure 4.16, computational time increases exponentially as the number of paths increases. In addition, convergence towards the forecasted budget is achieved for any number of paths that exceeds 1,000. Thus, 2,000 random paths were chosen as the number of iterations that are guaranteed to achieve model accuracy and optimize computational time. It was also assumed that the variation in the forecasted budget RV and computational time ctV for two consequent trials should not exceed 0.05% and 50%, respectively. In this case, the findings indicated that convergence towards the forecasted budget is achieved for any number of 187  paths exceeding 2,000, which was thus chosen as the number of iterations guaranteed to achieve model accuracy and optimize computational time.   ( ) ( )( )( ) ( )( )H trial A H trial BR H trial AE R E RV E R   (27)  ( ) ( )( )H trial A H trial Bct H trial Act ctV ct   (28)  Figure 4.16 Trade-off analysis between computational time and number of simulation paths  4.6.3 Results for LSD Method The forecasted budget inclusive of contingency ( )E R  was estimated for the benchmark scenario (Scenario-ESH) as $103.37 million, compared to $100.32 million as the planned base case excluding contingency. In this case, contingency was calculated at 3.05 million (3.05%), using the estimated 6% level of delay. For those two scenarios (Scenario-SEC and MEC)—implementing El Teniente layout and utilizing the conveyor system—the objective was to compare the forcasted 188  budget for the scenarios implementing side-sequencing versus middle-sequencing. Thus, since both models are characterized by 5% level of delay, the forecasted budgets are very similar at 103.01 and 103.04. These values are considered to be equal, despite minor differences, since the unit costs for each work package and level of delays were considered to be the same. Contingency was estimated for those two cases at approximately $2.71 million (2.71%), which is lower than the benchmark scenario. In contrast, in the Scenario-SOC, where offset herringbone layout is implemented, the cost base line excluding contingency was $99.64 million, which is lower than that of other scenarios utilizing the El Teniente layout. More specifically, at the 9% level of delay obtained from the DES models, the LSM model estimated the budget inclusive of contingency as 103.79 million, where the cost contingency is $4.15 million (4.16%). Fitted beta distributions for the four scenarios are depicted in Figure 4.17.  Figure 4.17 Beta distributions for the four flexible scenarios 189  4.7 Case Study: Project Comprising Multiple Work Packages  The scenario discussed herein is reflective of the actual New Afton project, with modified scale and features. Project conditions with respect to scope, time and cost parameters have been abstracted for illustrative purpose.   4.7.1 Model Input Parameter  Construction was expected to start in January 2008 and last for approximately nine years. The forecasted base case construction cost baseline was estimated at $335,500,000 Canadian dollars, exclusive of contingency allowance. The project consists of 18 major work packages, including development and construction within the bottom of the ore body footprint, as shown in Table 4.9 and Figure 4.18. For simplicity, yet without losing the essence of the richness of the case study, the planned development and construction schedule baseline was set at eight years and ten months (106 months). However, the project schedule could be extended up to maximum of ten years (120 months) to allow for simulating of actual schedule scenarios (paths).  Work packages were assumed to have fixed start date, and only durations can be extended. Moreover, work package durations and early start dates were rounded to the nearest month. As a further prerequisite, the first three work packages had to be completed before work on building those horizontal interdependent levels within the ore body footprint could commence. Development and construction results obtained from the DES benchmark model scenario were utilized in work packages 6 to 12 since each work package has different start date and duration. Using the scope of works and durations for individual work packages, planned work rates could be calculated. The resulting planned work rates and estimated unit cost for each work package are 190  shown in Table 4.9 and illustrated in Figure 4.18. In this calculation, it was assumed that the base case level of delays is 6% or 0 0 94 1( ; , . , )trif x , similar to the results for the benchmark model Scenario-ESH, even though each work package can have a unique schedule risk profile.   Figure 4.18 Work package parameter assignment matrix for a construction project comprising multiple work packages          Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 WP.1 (𝑞1, 𝑐1)                         WP.2 (𝑞2, 𝑐2)                       WP.3 (𝑞3, 𝑐3)                                 WP.4(𝑞4, 𝑐4)                               WP.5(𝑞5, 𝑐5)                            WP.6 (𝑞6, 𝑐6)                           WP.7 (𝑞7, 𝑐7)                          WP.8 (𝑞8, 𝑐8)                           WP.9 (𝑞9, 𝑐9)                          WP.10 (𝑞10, 𝑐10)                             WP.11 (𝑞11, 𝑐11)                 WP.12 (𝑞12, 𝑐12)              WP.13 (𝑞13, 𝑐13)                  WP.14  (𝑞14, 𝑐14)                       WP.15 (𝑞15, 𝑐15)  WP.16 (𝑞16, 𝑐16)                 WP.17 (𝑞17, 𝑐17)                 WP.18 (𝑞18, 𝑐18)            191  Table 4.9 Scope, time and cost parameters used in the LSM model for a construction project comprising multiple work packages ID Work Package Description Work Model Time Model Cost Model Scope of work 𝑄  Unit Work rate  𝑞   = 𝑄/𝑇 Start date   𝑥  months Duration  𝑇  months Unit cost   𝑐      $/work Cost  𝐶 Million $ Cost ratio (%) WP.1 Main Access Drift (Development) 4500 (m) 150 0 30 6,600 29.7 8.85 WP.2 Conveyor Drift (Development) 4500 (m) 125 0 36 6,600 29.7 8.85 WP.3 Conveyor Belt (Construction) 4500 (m) 125 2 36 9,200 41.4 12.34 WP.4 Footwall Drive (Development) 800 (m) 160 36 5 6,600 5.28 1.57 WP.5 Shop (Development) 390 (m) 65 38 6 9,300 3.63 1.08 WP.6 Apex Drive (Development) 4004 (m) 222 36 18 4,200 16.82 5.01 WP.7 Undercut Drive (Development) 3220 (m) 179 36 18 4,200 13.52 4.03 WP.8 Extraction Drive (Development) 4004 (m) 222 36 18 4,600 18.42 5.49 WP.9 Drawpoint Drift (Development) 3024 (m) 168 39 18 5,600 16.93 5.05 WP.10 Crosscut Drift (Development) 2012 (m) 112 39 18 5,600 11.27 3.36 WP.11 Undercut Strips (Construction) 378 (unit) 5.73 37 66 16,800 6.35 1.89 WP.12 Drawbells (Construction) 189 (unit) 2.86 40 66 90,000 17.01 5.07 WP.13 Haulage Drifts (Development) 3160 (m) 48 36 66 6,600 20.86 6.22 WP.14 Crusher Complex 1 (bulk unit) 0.167 48 6 15,000,000 15 4.47 WP.15 Ventilation Drives (Development) 1900 (m) 29 36 66 3,800 7.22 2.15 WP.16 Ventilation Raises (Development) 2800 (m) 58 0 48 8,000 22.4 6.68 WP.17 Ventilation Equipment* 1 (bulk unit) 0.03 0 36 10,000,000 10 2.98 WP.18 Mine services** 1 (bulk unit) 0.017 0 60 50,000,000 50 14.9 *Ventilation equipment includes surface fans, bulk headers, mine compressor, air heater, etc. **Mine services include electrical distribution system, dewatering, etc.  Underground Capital cost = $ 335.48 Million    192  4.7.2 Results for LSD Method The LSM algorithm was executed for the base case scenario at 6% level of delays. Planned and simulated aggregated remaining work versus time are depicted in Figure 4.19 for three of the 2,000 paths simulated. The expected total budget, inclusive of contingency, was estimated at $346.01 million by averaging the budget values versus the base budget of $335.50 million, as shown in the cumulative expenditure function presented in Figure 4.20. In this case, cost contingency was estimated at $10.51 million (3.13%).  Alternatively, contractors can choose the level of confidence that they feel comfortable with to derive the final estimated figure for the contingency reserve. Thus, a beta distribution fitted to the histogram is used to obtain the different values of contingencies pertaining to different confidence levels, as shown in Figure 4.22. Those contingency values can be obtained from the estimated beta distribution fitted to the budget histogram (Figure 4.21) using the minimum and maximum budget values of $335.37 and $368.10 million, respectively, along with the estimated beta parameters of 3 65 7 28( ; . , . )betaf x , as shown in Figure 4.22. Using the beta distribution function obtained for the budget, contingency reserve can be estimated for five different contractor confidence levels (for example, 50%, 60%, 70%, 80% and 90%). In this case, the budgets, inclusive of contingency, were estimated at $345.95, $347.18, $348.53, $350.14 and $352.39 million, respectively, compared to the base budget of $335.50 million, exclusive of contingency.   193   Figure 4.19 Planned versus simulated evolution for three paths of aggregated remaining work for a project comprising eighteen work packages  Figure 4.20 Cumulative capital expenditure for base case scenario for a project comprising eighteen work packages  194   Figure 4.21 Histogram of the budget for the base case scenario for a project comprising eighteen work packages   Figure 4.22 Beta distribution of the budget for a construction project comprising eighteen work packages  195  4.7.3 Sensitivity Analysis Sensitivity analysis was conducted for five different levels of delay (e.g., five different beta distribution functions). Here, it was assumed that, in the worst case scenario, the construction schedule is disrupted by 18%, which was the most likely value in the beta distribution (m = 0.82). In this case, delay was modeled as beta 4 54 1 82( ; . , . )betaf x , which is equivalent to 0 0 82 1( ; , . , )trif x . The best case scenario was modeled as 0 0 98 1( ; , . , )trif x , in which a 2% delay is expected (m = 0.98). For each of the five scenarios, LSM algorithm was run for 2,000 paths representing the aggregated remaining work; hence, the results are estimated for 2,000 different budget values, inclusive of contingency. The histograms of those 2,000 different values are arranged to fit beta distributions for these five scenarios representing different levels of delay, as shown in Figure 4.23.  Using the beta distribution function obtained for the budget for each scenario, contingency reserve was estimated for five different contractor confidence levels, as shown in Table 4.10. As can be seen, greater schedule uncertainty results in an increased expected budget. The model shows a linear trend, whereby contingency increases with a greater the risk of delays (Figure 4.24). For example, the optimistic case and pessimistic scenarios reveal contingencies at 50% confidence level of $5.94 million (1.8%) and $27.87 million (8.3%), respectively. They also indicate contingencies at 90% confidence level of $11.49million (3.4%) and $36.79 million (11.00%), respectively.       196  Table 4.10 Results for the budget, inclusive of contingency associated with schedule delays Schedule disruption scenarios  PERT Beta (𝛼, 𝛽) from         Tri (a,m,b) Budget Analysis & Statistics  Beta shape parameters (fitted values) Total Budget including Contingency ($Millions) Contractor Confidence level BETA 𝛼 BETA 𝛽 Minimum Budget ($Millions) Maximum Budget ($Millions) 50% 60% 70% 80% 90% Case 1 (Optimistic)  m=0.98  PERT Beta (3.54, 0.78) 2.34 7.47 $335.27 $363.26 Budget $341.44  Contingency $5.94 (1.8%) Budget $342.43  Contingency $6.93 (2.1%) Budget $343.56  Contingency $8.06 (2.4%) Budget $344.96  Contingency $9.46 (2.8%) Budget $346.99  Contingency $11.49 (3.4%) Case 2 (Base case) m=0.94  PERT Beta (3.89, 1.01) 3.65 7.28 $335.37 $368.10 Budget $345.96  Contingency $10.46 (3.1%) Budget $347.18  Contingency $11.68 (3.5%) Budget $348.53  Contingency $13.03 (3.9%) Budget $350.14  Contingency $14.64 (4.4%) Budget $352.39  Contingency $16.89 (5.0%) Case 3 m=0.90   PERT Beta (4.17, 1.27) 4.12 10.46 $337.90 $385.99 Budget $351.00  Contingency $15.5 (4.6%) Budget $352.47  Contingency $16.97 (5.1%) Budget $354.12  Contingency $18.62 (5.5%) Budget $356.1  Contingency $20.6 (6.1%) Budget $358.94  Contingency $23.44 (7.0%) Case 4 m=0.86 PERT Beta (4.39, 1.54) 3.52 9.23 $343.61  $393.42  Budget $356.76  Contingency $21.26 (6.3%) Budget $358.39  Contingency $22.89 (6.8%) Budget $360.20  Contingency $24.7 (7.4%) Budget $362.41  Contingency $26.91 (8.0%) Budget $365.57  Contingency $30.07 (9.0%) Case 5 (Pessimistic) m=0.82  PERT Beta (4.54, 1.82) 3.68 6.41 $347.96 $391.32 Budget $363.37  Contingency $27.87 (8.3%) Budget $365.09  Contingency $29.59 (8.8%) Budget $366.98  Contingency $31.48 (9.4%) Budget $369.21  Contingency $33.71 (10.0%) Budget $372.29  Contingency $36.79 (11.0%)  197    Figure 4.23 Beta distribution functions of the budget for five different delay levels      Figure 4.24 Percentage contingency for five different confidence levels   198  4.8 Discussion of the Results  Cost contingency is often used to manage uncertainties that would lead to schedule delays. While risks are shared between owners and contractors, depending on the type of contract agreed upon, in this work, cost contingency was addressed from contractor’s perspective and included allowances to compensate for schedule delays. In order to proactively manage schedule uncertainty, project manager should make timely decisions to execute construction crashing as an option to achieve planned schedule baseline. Thus, here, a method was developed, allowing project managers crashing decisions that respond to schedule uncertainties in construction projects integrated into the budget valuation from contractor’s perspective. This approach estimates a contingency allowance using the framework of real options and Monte Carlo simulation.  This conceptual simulations-based real options method can explicitly recognize the uncertainty involved in each project work package. This is achieved by developing a stochastic process that accounts for overlaps of multiple work packages comprising the project. More specifically, the model integrates the work package scope, time and cost parameters and associated random variables into a time-based function that estimates the aggregated remaining work function for the completion of the entire project. The core concept in the valuation is based on obtaining the optimized values of incurred budget at every time interval using regression analysis in which the value of timely decision of crashing option is selected based on the estimated level of delays. The results yielded by the LSM method for estimating contingency have been demonstrated for three numerical examples pertaining to projects including two, seven, and eighteen overlapping work packages. The results indicated that significant changes in capital budget allocation stem from variation in a contractor’s risk perception and confidence level of estimated delays.  199  Chapter 5: Conclusions and Future work  5.1 Conclusions This study aimed to investigate recognition, modeling, and pricing of flexible strategies that can be adopted in the design and planning of cave systems. This is a fundamental issue in planning and design, as being able to integrate flexibilities into this process not only helps control the negative aspects of uncertainties, but also improves the project economic value. Thus, the findings reported in this study are expected to provide the cave mining system management and planners a comprehensive approach for accommodating flexibilities that arise during the project planning and execution. An objective of this study is to provide state-of-the-art techniques and tools employed in planning that can be used to support decision-making processes in cave mining systems.  Three key types of flexibility, pertinent to the cost of the construction phase, are identified in this study. Each is related to a specific cave mining sub-system—undercut, extraction, or haulage level—and can be integrated and exercised separately or in combination with the other flexibilities in cave mining systems. Construction crashing has been shown to be achievable by utilizing the ore handling system in construction and improving mucking strategies, along with employing the El Teniente layout in order to enhance the material and equipment logistics. Also, the flexibility presented in the undercut level is capable of improving the rate of construction by implementing the advanced undercut middle-sequencing, which results in more expedient construction. These three flexibilities allow for providing additional open faces in every AUPC, as well as efficient management and effective utilization of equipment. However, 200  implementation of these flexibilities in cave mining operations (e.g., New Afton mine) requires considerations pertaining to the system planning and design and thus may require an upfront cost in the construction phase.   As this approach also allows conveying and traditional truck hauling to be used individually or simultaneously in the pre-production phase, it adds further flexibility, especially for small-size caving systems. By switching between the truck-haul and conveyor systems in the case of shutdowns, or even utilizing both systems in the case of fleet congestion along a decline access, construction performance can be significantly improved. This flexibility reduces the time required for completion of mucking activities, as well as reduces fleet congestion within any shared access declines. By prioritizing the construction schedule, it can be ensured that the conveyor system is available for use when additional crews and equipment are scheduled for developing multiple headings, as well as during the construction of multiple drawbells. In order to be able to use a conveyor system in the pre-production phase, when designing the major haulage components (e.g., crusher complex and conveyor chamber), it has to be ensured that these will be located near the undercut starting point. Moreover, the development of the haulage drifts has to be prioritized, to ensure that the required ore passes and vent raises can be built without any delays or interruptions.   In general, switching between the El Teniente and Offset Herringbone layout designs is not recommended because many design factors considered in the present study constrain the potential for transitioning from one to another during construction. Even though the El Teniente layout is characterized by longer crosscuts, and thus requires more extensive total drifting 201  compared to Offset Herringbone, it provides greater construction advantages in practice. More specifically, it helps in eliminating avoidable turnouts and reducing small-scale mining cycles, while also providing additional temporary access to development and construction zones. Thus, in case changing the design to Offset Herringbone during construction would result in any geotechnical, safety, or production advantages, the mine management can strategically plan to change the layout style in the subsequent ore blocks.   Owing to the technical restriction that demands the unavoidable coupling of the development of undercut and extraction levels in the advance undercut strategy, and having a specified working zone for each work package, construction acceleration can be achieved by altering the undercut strategy from side-sequencing to middle-sequencing. This flexibility allows for providing almost twice the number of available open faces and accesses to crosscuts within the stress shadow zone in the early and full stage of development in small size caving projects. Thus, construction crashing can be exercised by increasing equipment utilization. More specifically, if metal prices have declined to specific threshold levels, a mine operation can switch from middle-sequencing to side-sequencing and advance only in the high grade ore. Yet, the option to achieve a higher performance rate by progressing from both sides is available if metal prices increase.  With respect to modeling flexibilities, simulation techniques hold great promise, as they enable examining different alternatives, assist in incorporating strategic flexibilities into systems, and help obtain technical results required for economic valuations. Both economic and technical models can be easily implemented in practice, enabling mining companies to focus on maximizing the value of projects rather than minimizing the upfront capital. However, accuracy 202  of these models is dependent on the reliability of the input data. In practice, however, technical data regarding geotechnical and technical problems are not always complete and readily available before construction commences.   In this work, several models were developed utilizing ExtendSim© software to investigate the impact of implementing the aforementioned flexibilities on the development rates of multiple face headings. The investigation focused on the three interconnected infrastructure levels—apex, undercut and extraction—as well as the construction rates of drawbells and associated undercut strips. These models were developed based on the constraints imposed by adopting the advance undercut strategy using the DES method. Initially, simulation models were developed specifically for the development and construction of an existing mine and their complexity evolved as the work progressed. Model verification and validation were carried out to ensure that the input data and model assumptions were adequate, reasonable, and correct and were appropriate for developing the logic that would be used to build the models. The main goal was to guarantee that the final development and construction models were reliable and could thus be employed with confidence within the intended context.    Simulation results indicate that construction of drawbells is the critical path in narrow ore bodies. In addition, the results pertaining to the flexible models confirmed significant construction achievement, compared to benchmark models. Simulation model results further indicate that using the conveyor system early in the construction phase results in significant improvements in the construction speed and development advance rates. Likewise, the results obtained from changing the strategy of undercut sequencing from side-sequencing to middle-sequencing 203  indicate substantial improvements in the construction speed. The findings also suggest that development and construction rates are critically dependent on the number of machines employed; thus, equipment utilization must be optimized in order to achieve construction targets.   With respect to pricing of the flexibility discussed above, in this work, a conceptual simulation-based real options method was developed, enabling the users to calculate the budget inclusive of contingency and thus obtain the optimal value of a crashing option from a contractor’s perspective. The proposed method was able to respond to schedule uncertainty and compensate for schedule delays by incorporating the decision-making construction crashing strategies into the budget valuation. The value of this method stems from its ability to explicitly recognize the uncertainty involved in each work package and integrate project scope of work, duration and unit cost parameters into a single stochastic function. This approach allows estimating the percentage of the work that needs to be completed in the time remaining within the duration of the entire project.  The proposed LSM method was intended for incorporation into the project decision-making strategies in a mining company’s project valuation model aimed at mitigating schedule delays due to equipment and ground performance. This model is suitable for modeling American-style options, whereby the decision to implement crashing can be exercised at any time prior to the project completion date, as well as at the option maturity date. The results yielded by the DES models are used as input parameters in the LSM models, the results of which have been demonstrated for several overlapped work package scenarios abstracted from the DES benchmark and flexible scenarios. Moreover, as the LSM method implicitly recognized the 204  uncertainty involved in the construction schedule, the results confirm that significant change in costs stems from the variation in risk perceptions and confidence levels.  5.2 Future Work The following suggestions are considered as significant future work aimed at improving the planning methodologies for ensuring flexibility in cave mining systems: 1. The study presented in this work focused on identifying flexibilities that can assist in improving resource utilization in cases of multiple drifting in narrow ore bodies. Identification of potential flexibilities in a single heading is another area of research that can be implemented as a part of the development schedule. The goal of this initiative is being able to increase the size of major drifts (e.g., decline access or conveyor drifts), as well as accelerate the development by utilizing larger and more powerful equipment or two conventional sets of equipment concurrently.    2. Another recommended extension comprises improving the DES models by conducting major measurement campaign and time studies in order to provide more details of ground problem-related delays, activity durations and equipment shutdowns that can be integrated to improve the reliability of these models.   3. The LSM method can be extended by incorporating the critical path method (CPM) into the algorithm. In CPM, all work packages positioned on the critical path should be treated differently from non-critical activities. As each work package has unique attributes, 205  physical constraints, and associated risks, these can be captured by the extended model by incorporating the schedule network logic into the valuation process. 4. Another potential extension of the LSM model could be achieved by including the effect of inflation, unit cost variability, and currency exchange rate fluctuations. This extension would provide a complete and robust approach for estimating the budget, inclusive of cost contingency from a contractor’s perspective, which includes allowance for managing schedule delays and changes in unit cost parameters.    5. 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Journal of Management in Engineering, 6(4), 458-470.   221  Appendices  Appendix A   Dynamic Programing Optimization Results  A.1 Equipment Utilization for Four-drawbell Advance Undercut Progress Cycle Table A.1 Final results obtained for construction equipment (Four-Drawbell) Number of Machines Machine NO.1 Load-haul-dump Machine No. 2 Remote Explosive Machine No.3 Long-hole Drilling Machine No.4 Cable Bolting Machine No.5 In the hole Roger 8 UC strips (days) 4 DB (days) 8 UC strips (days) 4 DB (days) 8 UC strips (days) 4 DB (days) 8 UC strips (days) 4 DB (days) 8 UC strips (days) 4 DB (days) 1 50 111 50 89 50 89 19 62 19 48 2 50 91 50 89 26 62 19 48 19 48 3 50 89 NR NR 19 62 19 48 NR NR 4 50 89 NR NR 19 62 NR NR NR NR 5 NR NR NR NR NR NR NR NR NR NR  Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 New Afton Equipment Utilization 9 LHD used in development, construction and operation One Remote Explosive Machine Three Long-hole Drilling Machine Two Cable Bolting Machine One In the hole Roger Machine (UC) undercut , (DB) drawbell and (NR) not required  Table A.2 Detailed results obtained for construction equipment (Four-Drawbell) Stage 1 LHD / Trucks All other equipment types are set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 4 DB 2686 2685 2718 2660 2599 2664 2680 2664 2602 2660 2662 111   8 DB 1200 1200 1188 1188 1176 1188 1212 1188 1188 1188 1191 50  2 4 DB 2189 2175 2181 2164 2164 2183 2175 2167 2193 2160 2175 91   8 DB 1212 1200 1188 1176 1188 1212 1200 1356 1200 1176 1210 50  3 4 DB 2137 2133 2138 2133 2136 2130 2131 2157 2172 2132 2140 89   8 DB 1188 1188 1356 1200 1188 1177 1176 1212 1188 1188 1206 50  4 4 DB 2142 2144 2157 2155 2136 2136 2141 2140 2142 2134 2143 89   8 DB 1188 1188 1200 1188 1188 1188 1200 1356 1212 1200 1211 50 222    Stage 2 Remote explosive Machine LHD is set to be equal 3 and other equipment types are set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 4 DB 2137 2133 2138 2133 2136 2130 2131 2157 2172 2132 2140 89   8 DB 1188 1188 1356 1200 1188 1177 1176 1212 1188 1188 1206 50  2 4 DB 2135 2159 2182 2132 2132 2137 2131 2138 2159 2163 2147 89   8 DB 1212 1200 1224 1176 1188 1188 1188 1200 1368 1188 1213 51 Stage 3 Long-hole Machine LHD is set to be equal 3, Remote explosive machine is set to be 1 and other equipment types are set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 4 DB 2137 2133 2138 2133 2136 2130 2131 2157 2172 2132 2140 89   8 DB 1188 1188 1356 1200 1188 1177 1176 1212 1188 1188 1206 50  2 4 DB 1519 1496 1486 1486 1504 1493 1481 1490 1497 1511 1496 62   8 DB 612 612 612 600 600 624 744 624 612 612 625 26  3 4 DB 1483 1518 1497 1503 1473 1489 1488 1496 1503 1489 1494 62   8 DB 444 444 492 480 481 468 468 444 444 480 464 19  4 4 DB 1473 1486 1489 1474 1474 1486 1476 1478 1470 1504 1481 62   8 DB 384 360 384 384 372 384 384 372 372 384 378 16  Stage 4 Bolter machine LHD is set to be equal 3, Remote explosive machine is set to be equal 1, Long-hole machine is set to be equal 3 and other equipment types is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 4 DB 1486 1503 1502 1501 1491 1497 1473 1475 1475 1475 1488 62   8 DB 444 444 456 444 444 480 444 480 480 480 459 19  2 4 DB 1171 1158 1157 1152 1129 1156 1147 1148 1179 1166 1156 48   8 DB 444 444 480 444 444 444 444 444 480 469 453 19  3 4 DB 1171 1156 1151 1153 1164 1141 1173 1133 1150 1159 1155 48   8 DB 480 480 444 456 456 468 444 444 444 444 456 19 Stage 5 Roger machine LHD is set to be equal 3, Remote explosive machine is set to be equal 1, Long-hole machine is set to be equal 3, Bolter machine is set to be equal 2 and Roger machine is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 4 DB 1171 1158 1157 1152 1129 1156 1147 1148 1179 1166 1156 48   8 DB 444 444 480 444 444 444 444 444 480 469 453 19  2 4 DB 1289 1266 1263 1260 1262 1248 1250 1247 1261 1254 1260 52   8 DB 468 444 480 480 444 444 456 444 456 444 456 19   223  A.2 Equipment Utilization for Five-drawbell Advance Undercut Progress Cycle Table A.3 Final results obtained for construction equipment (Five-Drawbells) Number of Machines Machine NO.1 Load-haul-dump Machine No. 2 Remote Explosive Machine No.3 Long-hole Drilling Machine No.4 Cable Bolting Machine No.5 In the hole Roger 10 UC strips (days) 5 DB (days) 10 UC strips (days) 5 DB (days) 10 UC strips (days) 5 DB (days) 10 UC strips (days) 5 DB (days) 10 UC strips (days) 5 DB (days) 1 63 134 63 109 63 109 24 71 24 53 2 55 111 63 109 32 71 24 53 24 53 3 63 109 NR NR 24 71 25 53 NR NR 4 64 109 NR NR 20 72 NR NR NR NR 5 NR NR NR NR NR NR NR NR NR NR  Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 New Afton Equipment Utilization 9 LHD used in development, construction and operation One Remote Explosive Machine Three Long-hole Drilling Machine Two Cable Bolting Machine One In the hole Roger Machine (UC) undercut , (DB) drawbell and (NR) not required  Table A.4 Detailed results obtained for construction equipment (Five-Drawbells) Stage 1 LHD / Trucks All other equipment types is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 5 DB 3184 3273 3280 3192 3283 3285 3209 3186 3162 3205 3226 134   10 DB 1500 1524 1524 1512 1536 1536 1500 1512 1500 1512 1515 63  2 5 DB 2675 2659 2584 2610 2688 2678 2678 2677 2651 2651 2655 111   10 DB 1692 1692 1500 1512 1536 1536 1548 1524 1512 1512 1556 65  3 5 DB 2565 2662 2542 2665 2666 2671 2655 2553 2539 2567 2609 109   10 DB 1512 1524 1512 1536 1536 1524 1524 1512 1500 1500 1518 63  4 5 DB 2665 2544 2675 2544 2689 2661 2675 2609 2605 2536 2620 109   10 DB 1512 1500 1512 1500 1692 1536 1536 1500 1524 1500 1531 64           224  Stage 2 Remote explosive Machine LHD is set to be equal 3 and other equipment types is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 5 DB 2565 2662 2542 2665 2666 2671 2655 2553 2539 2567 2609 109   10 DB 1512 1524 1512 1536 1536 1524 1524 1512 1500 1500 1518 63  2 5 DB 2561 2690 2533 2615 2602 2664 2654 2656 2532 2549 2606 109   10 DB 1512 1524 1500 1524 1524 1525 1536 1524 1500 1524 1519 63  Stage 4 Bolter machine LHD is set to be equal 3, Remote explosive machine is set to be equal 1, Long-hole machine is set to be equal 3 and other equipment types is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 5 DB 1711 1702 1709 1708 1723 1708 1704 1702 1702 1692 1706 71   10 DB 588 588 600 576 588 600 588 588 576 588 588 24  2 5 DB 1272 1264 1279 1279 1266 1281 1289 1256 1267 1261 1271 53   10 DB 600 588 588 588 600 600 576 588 577 576 588 24  3 5 DB 1263 1270 1274 1276 1281 1274 1253 1301 1292 1276 1276 53   10 DB 588 588 588 600 588 588 588 588 600 576 589 25 Stage 5 Roger machine LHD is set to be equal 3, Remote explosive machine is set to be equal 1, Long-hole machine is set to be equal 3, Bolter machine is set to be equal 2 and Roger machine is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 5 DB 1272 1264 1279 1279 1266 1281 1289 1256 1267 1261 1271 53   10 DB 600 588 588 588 600 600 576 588 577 576 588 24  2 5 DB 1263 1266 1276 1276 1273 1268 1272 1264 1284 1301 1274 53   10 DB 588 576 588 576 588 600 588 600 576 600 588 24         225  A.3 Equipment Utilization for Ten-drawbell Advance Undercut Progress Cycle Table A.5 Final results obtained for construction equipment (Ten-Drawbells) Number of Machines Machine NO.1 Load-haul-dump Machine No. 2 Remote Explosive Machine No.3 Long-hole Drilling Machine No.4 Cable Bolting Machine No.5 In the hole Roger 20 UC strips (days) 10 DB (days) 20 UC strips (days) 10 DB (days) 20 UC strips (days) 10 DB (days) 20 UC strips (days) 10 DB (days) 20 UC strips (days) 10 DB (days) 1 125 265 127 204 127 204 29 114 29 84 2 126 206 127 204 63 114 34 91 29 83 3 127 204 NR NR 45 114 29 64 NR NR 4 126 204 NR NR 34 114 28 65 NR NR 5 NR NR NR NR 29 115 NR NR NR NR 6 NR NR NR NR NR NR NR NR NR NR  Same as side-sequencing Same as side-sequencing Changed from 3 to 5 equipment Changed from 2 to 3 equipment Same as side-sequencing  Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 (UC) undercut , (DB) drawbell and (NR) not required  Table A.6 Detailed results obtained for construction equipment (Ten-Drawbells) Stage 1 LHD / Trucks All other equipment is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 10 DB 6411 6325 6331 6330 6355 6372 6321 6324 6345 6378 6349 265   20 UC 3023 3011 3011 2987 2987 3023 2987 3023 3023 3023 3010 125  2 10 DB 4920 4949 4929 4926 4938 4988 4957 4923 4946 4925 4940 206   20 UC 3168 2999 3023 2987 3011 3023 3011 2987 3011 2999 3022 126  3 10 DB 4874 4902 4871 4915 4769 4946 4892 4922 4893 4928 4891 204   20 UC 2999 2999 3131 3167 2987 3107 2963 3023 2987 2999 3036 127  4 10 DB 4904 4818 4899 4897 4918 4915 4901 4932 4898 4925 4901 204   20 UC 2987 2999 3023 2999 2999 3011 2987 3011 3011 3167 3019 126 Stage 2 Remote explosive Machine LHD is set to be equal 3 and other equipment is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 10 DB 4874 4902 4871 4915 4769 4946 4892 4922 4893 4928 4891 204   20 UC 2999 2999 3131 3167 2987 3107 2963 3023 2987 2999 3036 127  2 10 DB 4945 4905 4868 4910 4884 4930 4904 4901 4895 4893 4904 204   20 UC 3023 3167 2975 3012 3011 3167 3023 3011 3011 2987 3039 127   226  Stage 3 Long-hole Machine LHD is set to be equal 3, Remote explosive machine is set to be equal 1 and Roger machine is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 10 DB 4874 4902 4871 4915 4769 4946 4892 4922 4893 4928 4891 204   20 UC 2999 2999 3131 3167 2987 3107 2963 3023 2987 2999 3036 127  2 10 DB 2743 2738 2735 2736 2742 2741 2738 2723 2758 2736 2739 114   20 UC 1523 1523 1511 1535 1523 1524 1523 1523 1523 1511 1522 63  3 10 DB 2743 2740 2736 2733 2740 2765 2747 2757 2750 2741 2745 114   20 UC 1031 1079 1079 1079 1092 1031 1091 1080 1043 1079 1068 45  4 10 DB 2737 2732 2738 2733 2740 2737 2765 2736 2733 2735 2739 114   20 UC 827 815 827 827 815 827 827 815 803 791 817 34  5 10 DB 2759 2739 2786 2736 2738 2770 2741 2751 2738 2737 2750 115   20 UC 671 755 683 732 671 683 683 695 683 683 694 29  6  2743 2738 2752 2733 2761 2741 2752 2736 2739 2752 2745 114    611 624 611 623 611 611 611 611 611 623 615 26  Stage 4 Bolter machine LHD is set to be equal 3, Remote explosive machine is set to be equal 1, Long-hole machine is set to be equal 5 and Roger machine is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 10 DB 2737 2732 2738 2733 2740 2737 2765 2736 2733 2735 2739 114   20 UC 827 815 827 827 815 827 827 815 803 791 817 34  2 10 DB 2161 2173 2178 2171 2183 2205 2188 2156 2207 2266 2189 91   20 UC 815 815 815 804 815 815 803 815 815 827 814 34  3 10 DB 2077 2065 2070 1923 1933 2003 2063 2005 1900 2059 2010 84   20 UC 671 683 671 743 743 683 683 683 755 671 699 29  4 10 DB 2066 2066 2063 2061 2062 1996 1980 2062 1991 2010 2036 85   20 UC 683 683 683 683 683 683 671 671 671 659 677 28 Stage 5 Roger machine LHD is set to be equal 3, Remote explosive machine is set to be equal 1, Long-hole machine is set to be equal 5, Bolter machine is set to be equal 3 and Roger machine is set to be equal 1  No. of machines  Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Average (hours) Average (days)  1 10 DB 2077 2065 2070 1923 1933 2003 2063 2005 1900 2059 2010 84   20 UC 671 683 671 743 743 683 683 683 755 671 699 29  2 10 DB 2008 1921 2071 2063 2070 1899 1906 2059 1894 2002 1990 83   20 UC 671 743 695 683 672 743 743 659 731 659 700 29       227  Appendix B  Discrete Event Simulation Results   B.1 The Benchmark Model  Table B.1 The Benchmark Development Model – The mean and standard deviation results for 10 random runs Apex Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 119 143 107 131 131 119 143 119 131 143 128.60 153.60 12.39 Tertiary  155 143 143 143 143 143 143 143 143 167 146.60 65.60 8.10 Quaternary 167 179 167 167 167 155 167 179 155 167 167.00 64.00 8.00 Quinary  203 203 191 215 191 215 203 192 215 203 203.10 93.43 9.67 Senary 252 251 251 251 251 239 239 251 239 251 247.50 34.50 5.87 Undercut Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 119 119 119 119 119 143 119 119 119 119 121.40 57.60 7.59 Tertiary  131 132 143 143 131 131 131 143 143 143 137.10 38.77 6.23 Quaternary 167 167 155 167 167 155 155 167 143 167 161.00 72.00 8.49 Quinary  191 203 215 203 180 203 203 179 215 191 198.30 162.23 12.74 Senary 251 239 251 239 251 227 227 239 251 239 241.40 89.60 9.47 Extraction Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 143 143 143 131 143 131 143 155 167 143 144.20 110.40 10.51 Tertiary  155 144 179 155 143 155 155 143 143 155 152.70 119.57 10.93 Quaternary 179 179 167 156 191 155 179 167 167 179 171.90 130.77 11.44 Quinary  203 203 227 215 203 215 204 203 239 203 211.50 159.83 12.64 Senary 287 287 287 287 275 275 287 287 287 287 284.60 25.60 5.06 Drawpoint Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 203 215 215 191 203 203 227 203 203 191 205.40 121.60 11.03 Tertiary  191 191 215 215 204 204 203 227 227 215 209.20 165.51 12.87 Quaternary 263 240 239 239 263 239 239 239 251 251 246.30 100.90 10.04 Quinary  263 239 251 251 251 251 251 251 251 275 253.40 89.60 9.47 Senary 335 323 323 323 323 311 311 323 323 323 321.80 46.40 6.81   228   Table B.2 The Benchmark Constructing Model (10-day mucking) – The mean and standard deviation results for 10 random runs Drawbell Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 876 861 862 861 857 855 871 860 851 892 864.73 143.33 11.97 Twin 926 931 958 937 936 930 926 934 957 928 936.14 137.09 11.71 Tertiary  1051 1056 1080 1001 1054 1003 1069 1001 1067 990 1037.22 1168.69 34.19 Quaternary 1133 1148 1153 1165 1151 1145 1145 1152 1142 1147 1147.94 67.79 8.23 Quinary  1261 1274 1291 1279 1296 1288 1260 1297 1271 1272 1278.99 185.36 13.61 Undercut Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 168 180 168 180 168 168 168 168 180 168 171.28 33.47 5.79 Twin 312 300 312 312 300 312 312 312 312 324 310.46 46.40 6.81 Tertiary  348 348 360 348 360 348 348 360 360 348 352.51 37.91 6.16 Quaternary 444 444 444 480 456 444 468 480 444 444 454.46 238.40 15.44 Quinary  588 588 576 588 588 576 576 600 600 588 586.58 77.08 8.78  Table B.3 The Benchmark Construction Model (5-day mucking) – The mean and standard deviation results for 10 random runs Drawbell Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 678 701 710 692 705 701 691 713 702 689 698.20 113.27 10.64 Twin 767 766 765 763 770 769 771 763 775 764 767.43 15.81 3.98 Tertiary  893 898 893 890 784 899 900 900 892 881 883.18 1258.88 35.48 Quaternary 971 964 984 970 977 963 966 969 971 992 972.77 82.16 9.06 Quinary  1099 1115 1136 1117 1096 1109 1118 1105 1085 1096 1107.48 212.91 14.59 Undercut Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 168 168 168 168 168 168 180 168 168 168 168.95 14.22 3.77 Twin 300 312 300 288 300 312 312 312 312 312 305.66 72.00 8.49 Tertiary  360 360 360 360 348 348 360 360 348 348 354.86 38.33 6.19 Quaternary 456 468 480 456 480 444 480 444 468 456 462.86 198.40 14.09 Quinary  588 588 576 588 588 577 588 588 576 588 584.23 32.64 5.71  229   B.2 Flexibility in the Ore Handling System Table B.4 Flexible Development Model – The mean and standard deviation results for 10 random runs Apex Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 107 107 107 107 107 107 107 84 107 107 107.00 52.9 7.27 Tertiary  107 107 107 107 107 95 107 119 107 107 107.00 32.00 5.66 Quaternary 107 119 119 119 107 108 107 119 119 119 114.30 36.90 6.07 Quinary  143 143 119 131 131 119 119 131 119 119 127.40 97.60 9.88 Senary 131 143 143 120 143 143 143 143 143 143 139.50 61.17 7.82 Undercut Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 96 95 107 83 83 83 107 107 107 96 96.40 110.04 10.49 Tertiary  83 107 95 83 83 83 83 96 83 83 87.90 72.10 8.49 Quaternary 107 107 107 107 107 107 107 107 107 108 114.30 0.10 0.32 Quinary  107 107 119 107 107 107 107 119 119 143 114.20 134.40 11.59 Senary 119 143 131 119 119 143 131 143 143 143 133.40 121.60 11.03 Extraction Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 119 119 119 119 131 119 119 119 119 119 120.20 14.40 3.79 Tertiary  143 131 131 120 143 131 131 143 143 143 135.90 66.77 8.17 Quaternary 143 155 143 131 131 143 143 143 143 143 141.80 46.40 6.81 Quinary  143 143 155 155 143 155 143 143 143 143 146.60 33.60 5.80 Senary 167 155 167 155 155 155 155 155 155 155 157.40 25.60 5.06 Drawpoint Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 167 167 155 167 167 203 167 167 167 167 169.40 153.60 12.39 Tertiary  167 167 179 179 179 179 179 179 179 191 177.80 46.40 6.81 Quaternary 203 203 191 167 203 168 191 191 203 203 192.30 200.90 14.17 Quinary  203 191 191 203 191 191 203 203 191 191 195.80 38.40 6.20 Senary 215 203 215 215 227 227 203 227 215 227 217.40 89.60 9.47    230  Table B.5 Flexible construction Model– The mean and standard deviation results for 10 random runs Drawbell Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 552 564 552 564 552 552 564 552 564 552 556.46 38.40 6.20 Twin 636 648 648 636 648 660 648 636 636 648 644.16 63.82 7.99 Tertiary  684 684 684 696 684 744 696 696 684 744 699.29 576.42 24.01 Quaternary 828 816 816 828 816 816 804 816 816 804 815.71 62.60 7.91 Quinary  972 960 972 960 948 960 972 960 984 948 963.26 129.60 11.38 Undercut Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 180 168 168 168 168 180 168 180 168 168 171.33 33.10 5.75 Twin 300 312 300 312 312 312 312 300 312 300 306.91 37.59 6.13 Tertiary  348 360 348 348 360 348 360 360 360 360 354.86 38.40 6.20 Quaternary 468 480 492 480 444 480 456 480 480 444 470.06 281.60 16.78 Quinary  588 564 588 576 588 588 576 576 600 576 581.69 102.97 10.15              231  B.3 Flexibility in the Extraction Level  Table B.6 Offset Herringbone development model (truck-haul system) – the mean and standard deviation results for 10 random runs Apex Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 143 119 119 143 131 131 143 143 119 119 131 128.00 11.31 Tertiary  143 143 143 143 143 155 143 143 143 143 144 14.4 3.79 Quaternary 167 203 167 167 167 167 167 167 167 167 171 129.6 11.38 Quinary  179 191 203 191 227 215 203 203 215 215 204 206.40 14.37 Senary 251 227 251 227 227 228 238 227 227 227 233 101.56 10.08 Undercut Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 119 119 119 119 119 119 119 119 119 119 120 14.4 3.79 Tertiary  119 119 119 119 131 155 119 119 119 119 124 134.40 11.59 Quaternary 167 167 155 167 155 155 167 155 155 155 160 38.40 6.20 Quinary  179 179 203 179 191 191 203 191 191 203 191 96.00 9.80 Senary 227 215 239 227 227 227 239 227 227 227 228 46.40 6.81 Extraction Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 143 119 143 143 143 143 132 119 155 143 138 132.90 11.53 Tertiary  155 143 143 155 143 143 143 155 143 143 147 33.60 5.80 Quaternary 179 179 167 167 167 167 167 179 179 167 172 38.40 6.20 Quinary  203 203 203 191 203 203 215 227 215 215 208 102.40 10.12 Senary 239 228 251 227 239 239 239 227 239 239 237 55.57 7.45 Drawpoint Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 191 215 227 215 227 192 228 203 227 215 214 204.44 14.30 Tertiary  227 227 239 227 239 239 227 227 227 227 231 33.60 5.80 Quaternary 263 263 251 263 275 263 275 263 263 275 265 57.60 7.59 Quinary  276 311 311 287 288 311 323 323 299 299 303 248.18 15.75 Senary 335 347 335 324 335 335 335 311 335 335 333 87.57 9.36       232  Table B.7 Offset Herringbone development model (conveyor system) – the mean and standard deviation results for 10 random runs Apex Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 107 107 107 107 107 107 107 84 107 107 107 52.9 7.27 Tertiary  96 107 84 107 107 107 107 107 107 107 104 59.38 7.71 Quaternary 107 107 119 119 107 107 107 107 107 107 109 25.60 5.06 Quinary  107 119 119 119 143 143 119 119 119 119 123 129.60 11.38 Senary 143 143 143 131 143 143 143 143 143 119 139 65.60 8.10 Undercut Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 83 83 83 107 83 107 83 83 83 107 90 134.40 11.59 Tertiary  107 83 83 96 107 107 83 107 83 84 94 140.44 11.85 Quaternary 95 95 95 95 95 95 95 95 95 95 95 0.00 0.00 Quinary  107 107 107 107 107 108 107 107 107 119 108 14.23 3.77 Senary 143 107 131 107 120 131 119 119 119 119 122 121.17 11.01 Extraction Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 131 119 119 119 119 119 119 119 119 119 120 14.40 3.79 Tertiary  119 143 143 131 119 119 131 119 119 131 127 97.60 9.88 Quaternary 143 131 131 119 119 131 143 143 143 131 133 89.60 9.47 Quinary  143 143 143 143 143 143 143 143 143 143 143 0.00 0.00 Senary 168 155 144 155 167 155 143 155 155 143 154 79.11 8.89 Drawpoint Drive (Model) Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Twin 191 168 167 179 179 179 167 179 179 191 178 76.10 8.72 Tertiary  179 179 191 191 179 191 227 191 179 191 190 206.40 14.37 Quaternary 203 191 204 215 191 204 215 215 215 191 204 110.04 10.49 Quinary  227 227 215 204 203 228 227 215 227 227 220 100.44 10.02 Senary 263 227 215 239 227 239 227 228 239 227 233 166.77 12.91     233  B.4 Flexibility in the Undercut Level   Table B.8 Middle-sequencing Construction Model (Case 1)– The mean and standard deviation results for 10 random runs (10-day mucking Drawbells) Drawbell Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 876 861 862 861 857 855 871 860 851 892 865 143.33 11.97 Twin 926 931 958 937 936 930 926 934 957 928 936 137.09 11.71 Tertiary  1051 1056 1080 1001 1054 1003 1069 1001 1067 990 1037 1168.69 34.19 Quaternary 1133 1148 1153 1165 1151 1145 1145 1152 1142 1147 1148 67.79 8.23 Quinary  1261 1274 1291 1279 1296 1288 1260 1297 1271 1272 1279 185.36 13.61 Senary  1455 1468 1457 1496 1449 1460 1463 1459 1475 1477 1466 187.81 13.70 Septenary 1740 1749 1755 1745 1757 1744 1736 1594 1744 1741 1731 2332.15 48.29 Octonary 1895 1922 1931 1917 1916 1918 1965 1911 1916 1918 1921 321.88 17.94 Nonary 2005 2052 2106 2067 2088 2056 1995 2121 2068 2073 2063 1570.77 39.63 Denary 2348 2289 2395 2278 2366 2352 2323 2355 2364 2354 2342 1286.93 35.87 Undercut Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 168 180 168 180 168 168 168 168 180 168 171 33.47 5.79 Twin 312 300 312 312 300 312 312 312 312 324 310 46.40 6.81 Tertiary  348 348 360 348 360 348 348 360 360 348 353 37.91 6.16 Quaternary 444 444 444 480 456 444 468 480 444 444 454 238.40 15.44 Quinary  588 588 576 588 588 576 576 600 600 588 587 77.08 8.78 Senary  624 636 624 636 624 636 636 636 636 648 633 57.60 7.59 Septenary 780 768 768 768 792 780 769 780 780 768 775 68.91 8.30 Octonary 899 899 923 899 899 887 911 911 887 911 903 129.60 11.38 Nonary 947 935 959 959 936 959 947 947 947 947 948 75.57 8.69 Denary 1079 1043 1043 1043 1079 1043 1043 1031 1079 1043 1053 345.60 18.59       234  Table B.9 Middle-sequencing Construction Model (Case1) – The mean and standard deviation results for 10 random runs (5-day mucking Drawbells)  Drawbell Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 678 701 710 692 705 701 691 713 702 689 698 113.27 10.64 Twin 767 766 765 763 770 769 771 763 775 764 767 15.81 3.98 Tertiary  893 898 893 890 784 899 900 900 892 881 883 1258.88 35.48 Quaternary 971 964 984 970 977 963 966 969 971 992 973 82.16 9.06 Quinary  1099 1115 1136 1117 1096 1109 1118 1105 1085 1096 1107 212.91 14.59 Senary  1175 1173 1167 1165 1167 1178 1174 1167 1168 1169 1170 18.90 4.35 Septenary 1366 1367 1316 1314 1326 1336 1325 1329 1374 1371 1342 586.04 24.21 Octonary 1499 1518 1510 1506 1517 1509 1493 1511 1487 1507 1506 99.34 9.97 Nonary 1577 1597 1666 1581 1598 1571 1590 1656 1604 1588 1603 1046.40 32.35 Denary 1751 1744 1765 1758 1744 1758 1756 1761 1756 1756 1755 46.10 6.79 Undercut Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 168 168 168 168 168 168 180 168 168 168 169 14.22 3.77 Twin 300 312 300 288 300 312 312 312 312 312 306 72.00 8.49 Tertiary  360 360 360 360 348 348 360 360 348 348 355 38.33 6.19 Quaternary 456 468 480 456 480 444 480 444 468 456 463 198.40 14.09 Quinary  588 588 576 588 588 577 588 588 576 588 584 32.64 5.71 Senary  743 623 623 623 623 755 623 623 624 635 650 2771.83 52.65 Septenary 767 779 767 767 767 791 779 767 779 767 773 72.00 8.49 Octonary 780 911 900 911 899 911 923 911 923 911 898 1780.44 42.20 Nonary 959 947 959 935 959 971 971 959 959 959 958 110.40 10.51 Denary 1079 1091 1043 1043 1043 1079 1043 1055 1103 1043 1062 550.40 23.46        235  Table B.10 Middle-Sequencing Flexible Construction Model (Case 1) – The mean and standard deviation results for 10 random runs (Undercut) Drawbell Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 552 564 552 564 552 552 564 552 564 552 556 38.40 6.20 Twin 636 648 648 636 648 660 648 636 636 648 644 63.82 7.99 Tertiary  731 767 755 743 743 743 767 755 755 731 749 168.00 12.96 Quaternary 863 851 863 851 851 851 863 863 839 863 856 70.40 8.39 Quinary  971 971 947 959 971 959 959 947 959 959 960 78.40 8.85 Senary  1055 1055 1067 1043 1067 1055 1067 1067 1055 1055 1059 65.60 8.10 Septenary 1259 1175 1259 1259 1187 1175 1163 1247 1259 1247 1223 1760.00 41.95 Octonary 1356 1355 1343 1367 1355 1367 1367 1367 1367 1343 1359 96.90 9.84 Nonary 1463 1475 1463 1463 1463 1475 1463 1475 1428 1439 1461 242.23 15.56 Denary 1619 1619 1631 1608 1608 1631 1607 1607 1631 1619 1618 105.78 10.28 Undercut Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 180 168 168 168 168 180 168 180 168 168 171 33.10 5.75 Twin 300 312 300 312 312 312 312 300 312 300 307 37.59 6.13 Tertiary  347 359 359 347 348 347 359 359 347 347 352 37.43 6.12 Quaternary 467 479 443 479 479 455 443 479 468 492 468 275.38 16.59 Quinary  587 587 587 587 575 587 587 575 587 575 583 33.60 5.80 Senary  635 623 743 635 635 635 623 635 623 743 653 2280.00 47.75 Septenary 779 767 779 767 767 767 767 779 767 767 771 33.60 5.80 Octonary 899 911 923 899 899 835 899 911 923 911 901 626.67 25.03 Nonary 959 971 959 947 947 959 959 960 947 947 956 66.50 8.15 Denary 1079 1043 1079 1043 1103 1103 1091 1091 1091 1079 1080 462.40 21.50       236  Table B.11 Middle-sequencing Construction Model (Case 2) – The mean and standard deviation results for 10 random runs (10-day mucking drawbells) Drawbell Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 851 875 851 852 851 875 857 880 856 875 862 150.46 12.27 Twin 938 931 924 925 922 929 927 930 925 928 928 20.54 4.53 Tertiary  1053 955 954 942 957 956 993 943 967 945 967 1143.17 33.81 Quaternary 1157 1149 1121 1144 1140 1147 1144 1172 1152 1170 1150 217.60 14.75 Quinary  1249 1253 1269 1254 1282 1260 1263 1255 1250 1251 1259 107.38 10.36 Senary  1298 1317 1311 1298 1291 1274 1294 1292 1294 1289 1296 139.51 11.81 Septenary 1503 1477 1529 1526 1485 1473 1471 1471 1438 1393 1477 1612.04 40.15 Octonary 1681 1656 1600 1605 1666 1652 1696 1691 1687 1669 1660 1138.68 33.74 Nonary 1721 1760 1745 1746 1735 1729 1727 1738 1731 1739 1737 126.54 11.25 Denary 2076 1889 1987 2066 2052 1987 1996 1991 2052 2067 2016 3347.57 57.86 Undercut Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 167 168 167 179 167 167 167 167 167 167 168 14.23 3.77 Twin 215 203 216 215 215 215 215 215 215 215 214 14.77 3.84 Tertiary  299 311 311 311 311 311 299 299 299 311 306 38.40 6.20 Quaternary 359 359 347 347 347 347 359 347 359 359 353 40.00 6.32 Quinary  396 407 407 395 407 395 384 383 395 395 396 75.38 8.68 Senary  444 479 443 443 479 455 455 479 443 455 458 246.50 15.70 Septenary 527 503 503 503 491 503 503 491 491 491 501 121.60 11.03 Octonary 599 587 587 587 587 575 587 575 575 587 585 57.60 7.59 Nonary 635 635 635 623 623 635 635 635 612 636 630 67.38 8.21 Denary 695 743 695 683 683 671 671 659 672 684 686 534.04 23.11       237  Table B.12 Middle-sequencing Construction Model (Case 2) – The mean and standard deviation results for 10 random runs (5-day mucking drawbells)   Drawbell Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 688 688 703 707 709 708 700 675 700 700 698 118.62 10.89 Twin 755 765 775 761 767 783 767 771 76- 766 691 64.44 8.03 Tertiary  880 794 783 883 792 780 780 780 780 881 813 2230.01 47.22 Quaternary 947 940 960 943 964 962 957 955 957 942 953 79.12 8.90 Quinary  971 967 964 971 969 977 965 969 974 967 969 16.04 4.01 Senary  1131 1111 1122 1120 1154 1132 1123 1121 1138 1127 1128 140.54 11.86 Septenary 1372 1178 1366 1172 1165 1166 1166 1368 1376 1371 1270 11265.11 106.14 Octonary 1495 1494 1493 1486 1508 1495 1508 1517 1505 1495 1500 88.49 9.41 Nonary 1574 1570 1570 1573 1576 1574 1568 1570 1565 1565 1571 14.28 3.78 Denary 1675 1573 1606 1673 1686 1597 1584 1673 1599 1584 1625 2079.56 45.60 Undercut Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 179 167 155 179 167 167 167 155 179 167 168 78.40 8.85 Twin 204 215 227 215 215 215 227 215 227 215 218 54.50 7.38 Tertiary  311 311 311 299 311 311 299 299 311 299 306 38.40 6.20 Quaternary 347 347 359 363 347 347 359 359 347 359 353 46.93 6.85 Quinary  407 395 407 407 395 407 395 407 395 395 401 40.00 6.32 Senary  420 443 443 455 443 503 443 443 476 443 451 521.07 22.83 Septenary 468 491 515 491 503 527 503 503 491 503 500 250.50 15.83 Octonary 587 575 587 587 575 587 587 575 587 575 582 38.40 6.20 Nonary 624 623 623 623 635 623 635 635 611 623 626 57.17 7.56 Denary 671 683 671 683 683 683 683 683 671 671 678 38.40 6.20       238  Table B.13 Middle-Sequencing Flexible Construction Model (Case 2) – The mean and standard deviation results for 10 random runs (Undercut) Drawbell Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 563 551 563 563 552 551 563 563 539 563 557 70.77 8.41 Twin 647 647 647 635 647 647 635 647 647 647 645 25.60 5.06 Tertiary  683 695 731 671 683 683 695 695 683 683 690 262.40 16.20 Quaternary 803 815 816 803 815 815 815 803 815 815 812 34.50 5.87 Quinary  863 863 851 863 863 863 851 863 863 851 859 33.60 5.80 Senary  995 983 983 983 971 983 983 996 995 995 987 67.57 8.22 Septenary 1247 1259 1055 1067 1055 1055 1259 1259 1271 1271 1180 11046.40 105.10 Octonary 1355 1367 1355 1355 1355 1355 1355 1343 1355 1355 1355 32.00 5.66 Nonary 1439 1439 1451 1463 1451 1463 1439 1451 1451 1451 1450 78.40 8.85 Denary 1535 1463 1499 1475 1487 1475 1487 1487 1475 1499 1488 398.40 19.96 Undercut Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Mean µ𝒊  (hours) Variance Standard deviation 𝝈𝒊 (hours) Primary 167 167 155 167 167 167 179 167 167 179 168 46.40 6.81 Twin 227 227 227 215 215 227 215 215 215 215 220 38.40 6.20 Tertiary  299 300 311 311 300 311 311 311 311 299 306 35.38 5.95 Quaternary 347 347 347 347 347 359 359 347 347 347 349 25.60 5.06 Quinary  395 407 407 395 395 395 407 407 407 395 401 40.00 6.32 Senary  455 443 467 455 443 479 479 455 455 443 457 185.60 13.62 Septenary 491 491 503 503 503 503 491 503 503 503 499 33.60 5.80 Octonary 587 575 575 599 587 587 587 575 575 575 582 70.40 8.39 Nonary 623 611 635 635 635 611 635 635 647 635 630 134.40 11.59 Denary 684 671 695 671 683 683 643 671 671 683 676 195.39 13.98     

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